System and method for predicting performance of electrical power cables

ABSTRACT

A computer simulation method is disclosed for simulating an electrical cable having a stranded conductor surrounded by a conductor shield encased in an insulation jacket and having an interstitial void volume in the region of the conductor injected with a fluid composition comprising at least one dielectric enhancement fluid component so as to at least partially fill the interstitial void volume at an initial time. The simulation method comprises for a selected length of the simulated cable, defining a plurality of radially arranged finite volumes extending the selected length of the simulated cable, and estimating the radial temperature of each finite volume. For a selected time period after the initial time, performing a series of steps at least once and outputting or otherwise using the value of the new concentration for the dielectric enhancement fluid component within each finite volume.

CROSS REFERENCE TO RELATED APPLICATION(S)

This application is a divisional of U.S. patent application Ser. No.11/468,118 filed Aug. 29, 2006 and claims priority benefit of U.S.provisional applications Ser. No. 60/712,309 filed Aug. 30, 2005 andSer. No. 60/712,944 filed Aug. 30, 2005.

FIELD OF THE INVENTION

The present invention relates to a method for extending the longevity ofan electrical power cable. More particularly, the invention relates to acomputer simulation method for predicting the long-term dielectricperformance of an in-service electrical cable segment which has beenrestored by injecting a dielectric enhancing fluid into the interstitialvoid volume of the cable.

BACKGROUND OF THE INVENTION

The gradual deterioration, and eventual failure, of electrical cables,such as those used in underground residential distribution circuits(URD), is well known. Failure of such cables, which generally comprise astranded conductor surrounded by a semi-conducting conductor shield, apolymeric insulation jacket, and an insulation shield, is primarilyattributed to high electrical fields within the insulation jacket aswell as long term exposure thereof to environmental moisture. Sincereplacing an underground cable is costly, a cable which has eitheractually failed, or is likely to do so in the near term based onstatistical data, is often treated (rejuvenated) to restore thedielectric integrity of its insulation, thereby extending its usefullife in a cost-effective manner. A typical method for treating such anin-service cable comprises introducing a tree retardant fluid into thevoid space (interstitial void volume) associated with the strandconductor geometry. This fluid is generally selected from a particularclass of aromatic alkoxysilanes which can polymerize within the cable'sinterstitial void volume as well as within the insulation by reactingwith adventitious water (see, for example, U.S. Pat. Nos. 4,766,011,5,372,840 and 5,372,841). Such a method (herein referred to as a“low-pressure” restorative method) typically leaves a fluid reservoirpressurized at no more than about 30 psig (pounds per square inch gage)connected to the cable for a 60 to 90 day “soak period” to allow thefluid to penetrate (i.e., diffuse into) the cable insulation and therebyrestore the dielectric properties.

Those skilled in the art of cable restoration currently have limitedability to predict the efficacy of one of the above low-pressurerestorative methods in their quest for improved fluid compositions andoptimized parameters. Moreover, this assessment of efficacy istime-consuming and generally limited to results on a particularcable/fluid combination operating under relatively specific conditions.For example, a current procedure utilized in the art to determine theperformance of a fluid (or fluid mixture) requires that each candidatefluid is injected into a laboratory cable which is then subjected to anexpensive and multi-month accelerated aging regimen at a singletemperature, whereupon it is sacrificed in an AC breakdown (ACBD) orimpulse breakdown test and also subjected to analysis of theconcentration profile of the fluid's components. Unfortunately, thisaccelerated aging method does not address the impact of real worlddynamic cable temperature variation and it has been shown to result inerrors in the range of an order of magnitude when used to predict actualcable ACBD field performance. (See Bertini, “Accelerated Aging ofRejuvenated Cables—Part I”, IEEE/PES/ICC Apr. 19, 2005 and Bertini,“Accelerated Aging of Rejuvenated Cables—Part II”, IEEE/PES/ICC Nov. 1,2006.)

SUMMARY OF THE INVENTION

A computer simulation method is disclosed for simulating an electricalcable having a stranded conductor surrounded by a conductor shieldencased in an insulation jacket and having an interstitial void volumein the region of the conductor injected with a fluid compositioncomprising at least one dielectric enhancement fluid component so as toat least partially fill the interstitial void volume at an initial time.The simulation method comprises:

-   for a selected length of the simulated cable, defining a plurality    of radially arranged finite volumes extending the selected length of    the simulated cable;-   estimating the radial temperature of each finite volume;-   for a selected time period after the initial time, performing at    least once each of:

calculating the change in mass of the dielectric enhancement fluidcomponent within each finite volume due to chemical reactions;

calculating the diffusion properties of the dielectric enhancement fluidcomponent within each finite volume;

calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid component within the finitevolumes; and

combining the calculated change in mass of the dielectric enhancementfluid component within each finite volume due to chemical reactions withthe calculated mass flux between each adjacent finite volume for thedielectric enhancement fluid component within the finite volumes todetermine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; and

-   outputting the value of the new concentration for the dielectric    enhancement fluid component within each finite volume.

The computer simulation method can further include:

using the outputted value of the new concentration for the dielectricenhancement fluid component within each finite volume to determine afirst calculated concentration profile for the dielectric enhancementfluid component within the conductor shield and the insulation jacket ofthe simulated cable for the selected time period after the initial time;

determining a constant radial temperature for each finite volume thatresults in a second calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for the selected time periodafter the initial time that approximates the first calculatedconcentration profile, by:

-   -   selecting a constant radial temperature for each finite volume        to use in determining the second calculated concentration        profile;    -   using the selected constant radial temperature, for a selected        time period after the initial time, performing at least once        each of:        -   calculating the change in mass of the dielectric enhancement            fluid component within each finite volume due to chemical            reactions;        -   calculating the diffusion properties of the dielectric            enhancement fluid component within each finite volume;        -   calculating the mass flux from one finite volume to another            finite volume for the dielectric enhancement fluid component            within the finite volumes;        -   combining the calculated change in mass of the dielectric            enhancement fluid component within each finite volume due to            chemical reactions with the calculated mass flux between            each adjacent finite volume for the dielectric enhancement            fluid component within the finite volumes to determine a new            concentration for the dielectric enhancement fluid component            within each finite volume;    -   outputting the value of the new concentration for the dielectric        enhancement fluid component within each finite volume using the        selected constant radial temperature;    -   using the outputted value of the new concentration for the        dielectric enhancement fluid component within each finite volume        using the selected constant radial temperature to determine the        second calculated concentration profile;    -   determining if the second calculated concentration profile        approximates the first calculated concentration profile;    -   if the selected constant radial temperature does not result in        the second calculated concentration profile being determined to        approximate the first calculated concentration profile,        selecting a new constant radial temperature to use in        determining the second calculated concentration profile; and    -   if the selected constant radial temperature does result in the        second calculated concentration profile being determined to        approximate the first calculated concentration profile, using        the selected constant radial temperature as a flux-weighted        temperature.

The computer simulation method can include using the flux-weightedtemperature to select a suitable fluid composition for injection intothe electrical cable being simulated.

In lieu of or in addition to outputting the value of the newconcentration, the computer simulation method can use the newconcentration for the dielectric enhancement fluid component within eachfinite volume to determine a calculated concentration profile for thedielectric enhancement fluid component within the conductor shield andthe insulation jacket of the simulated cable for the selected timeperiod after the initial time, and use the calculated concentrationprofile to select a suitable fluid composition for injection into theelectrical cable being simulated.

The computer simulation method can further include providing anempirical model of the dielectric performance of the simulated cable asa function of concentration of the dielectric enhancement fluidcomponent, and using the empirical model and the calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable to determine an estimate of dielectric performance changes fortimes after the initial time.

In yet another embodiment, a computer simulation method is disclosed forsimulating an electrical cable having a stranded conductor surrounded bya conductor shield encased in an insulation jacket and having aninterstitial void volume in the region of the conductor injected with afluid composition comprising at least one dielectric enhancement fluidcomponent so as to at least partially fill the interstitial void volumeat an initial time. The simulation method comprises:

-   for a selected length of the simulated cable, defining a plurality    of radially arranged finite volumes extending the selected length of    the simulated cable;-   estimating the radial temperature of each finite volume;-   for a selected time period after the initial time, performing at    least once each of:    -   calculating the diffusion properties of the dielectric        enhancement fluid component within each finite volume;    -   calculating the mass flux from one finite volume to another        finite volume for the dielectric enhancement fluid component        within the finite volumes; and    -   combining the calculated change in mass of the dielectric        enhancement fluid component within each finite volume with the        calculated mass flux between each adjacent finite volume for the        dielectric enhancement fluid component within the finite volumes        to determine a new concentration for the dielectric enhancement        fluid component within each finite volume; and-   outputting the value of the new concentration for the dielectric    enhancement fluid component within each finite volume.

The computer simulation method can further include:

-   using the outputted value of the new concentration for the    dielectric enhancement fluid component within each finite volume to    determine a first calculated concentration profile for the    dielectric enhancement fluid component within the conductor shield    and the insulation jacket of the simulated cable for the selected    time period after the initial time;-   determining a constant radial temperature for each finite volume    that results in a second calculated concentration profile for the    dielectric enhancement fluid component within the conductor shield    and the insulation jacket of the simulated cable for the selected    time period after the initial time that approximates the first    calculated concentration profile, by:    -   selecting a constant radial temperature for each finite volume        to use in determining the second calculated concentration        profile;    -   using the selected constant radial temperature, for a selected        time period after the initial time, performing at least once        each of:        -   calculating the diffusion properties of the dielectric            enhancement fluid component within each finite volume;        -   calculating the mass flux from one finite volume to another            finite volume for the dielectric enhancement fluid component            within the finite volumes;        -   combining the calculated change in mass of the dielectric            enhancement fluid component within each finite volume with            the calculated mass flux between each adjacent finite volume            for the dielectric enhancement fluid component within the            finite volumes to determine a new concentration for the            dielectric enhancement fluid component within each finite            volume;    -   outputting the value of the new concentration for the dielectric        enhancement fluid component within each finite volume using the        selected constant radial temperature;    -   using the outputted value of the new concentration for the        dielectric enhancement fluid component within each finite volume        using the selected constant radial temperature to determine the        second calculated concentration profile;    -   determining if the second calculated concentration profile        approximates the first calculated concentration profile;    -   if the selected constant radial temperature does not result in        the second calculated concentration profile being determined to        approximate the first calculated concentration profile,        selecting a new constant radial temperature to use in        determining the second calculated concentration profile; and    -   if the selected constant radial temperature does result in the        second calculated concentration profile being determined to        approximate the first calculated concentration profile, using        the selected constant radial temperature as a flux-weighted        temperature.

The computer simulation method can include using the flux-weightedtemperature to select a suitable fluid composition for injection intothe electrical cable being simulated.

In lieu of or in addition to outputting the value of the newconcentration, the computer simulation method can use the newconcentration for the dielectric enhancement fluid component within eachfinite volume to determine a calculated concentration profile for thedielectric enhancement fluid component within the conductor shield andthe insulation jacket of the simulated cable for the selected timeperiod after the initial time, and use the calculated concentrationprofile to select a suitable fluid composition for injection into theelectrical cable being simulated.

The computer simulation method can further include providing anempirical model of the dielectric performance of the simulated cable asa function of concentration of the dielectric enhancement fluidcomponent, and using the empirical model and the calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable to determine an estimate of dielectric performance changes fortimes after the initial time.

In alternative embodiments, the computer simulation methods noted can atleast partially fill the interstitial void volume at an initial timet=0, and perform the steps described for the selected time period foreach of a plurality of different selected incremental time periodsoccurring after t=0.

In the described embodiments, the finite volumes can be a plurality ofcoaxial cylinders extending the selected length of the simulated cable.

In the described embodiments, the computer simulation method cansimulate injection with a fluid composition comprising a plurality ofdielectric enhancement fluid components. For the selected time periodafter the initial time, the steps are performed at least once for eachof the dielectric enhancement fluid components.

A computer simulation system is also disclosed for simulating anelectrical cable having a stranded conductor surrounded by a conductorshield encased in an insulation jacket and having an interstitial voidvolume in the region of the conductor injected with a fluid compositioncomprising at least one dielectric enhancement fluid component so as toat least partially fill the interstitial void volume at an initial time.The system comprises:

-   means for defining a plurality of radially arranged finite volumes    extending the selected length of the simulated cable for a selected    length of the simulated cable;-   means for estimating the radial temperature of each finite volume;-   means for calculating the diffusion properties of the dielectric    enhancement fluid component within each finite volume for the    selected time period after the initial time using the estimated    radial temperature of each finite volume;-   means for calculating the mass flux from one finite volume to    another finite volume for the dielectric enhancement fluid component    within the finite volumes for the selected time period after the    initial time using the estimated radial temperature of each finite    volume;-   means for combining the calculated change in mass of the dielectric    enhancement fluid component within each finite volume due to    chemical reactions with the calculated mass flux between each    adjacent finite volume for the dielectric enhancement fluid    component within the finite volumes for the selected time period    after the initial time to determine a new concentration for the    dielectric enhancement fluid component within each finite volume;    and-   means for outputting the value of the new concentration for the    dielectric enhancement fluid component within each finite volume.    The computer simulation system can also include means for    calculating the change in mass of the dielectric enhancement fluid    component within each finite volume due to chemical reactions for a    selected time period after the initial time using the estimated    radial temperature of each finite volume, and means for combining    the calculated change in mass of the dielectric enhancement fluid    component within each finite volume due to chemical reactions with    the calculated mass flux between each adjacent finite volume for the    dielectric enhancement fluid component within the finite volumes for    the selected time period after the initial time to determine a new    concentration for the dielectric enhancement fluid component within    each finite volume.

The computer simulation system can also include means for using theoutputted value of the new concentration for the dielectric enhancementfluid component within each finite volume to determine a calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable for the selected time period after the initial time to select asuitable fluid composition for injection into the electrical cable beingsimulated.

The computer simulation system can also include means for storing anempirical model of the dielectric performance of the simulated cable asa function of concentration of the dielectric enhancement fluidcomponent, and means for using the empirical model and the calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable to determine an estimate of dielectric performance changes fortimes after the initial time.

The computer simulation system can also include:

-   means for using the outputted value of the new concentration for the    dielectric enhancement fluid component within each finite volume to    determine a first calculated concentration profile for the    dielectric enhancement fluid component within the conductor shield    and the insulation jacket of the simulated cable for the selected    time period after the initial time;-   means for storing a constant radial temperature for each finite    volume that results in a second calculated concentration profile for    the dielectric enhancement fluid component within the conductor    shield and the insulation jacket of the simulated cable for the    selected time period after the initial time that approximates the    first calculated concentration profile;-   means for calculating the diffusion properties of the dielectric    enhancement fluid component within each finite volume for the    selected time period after the initial time using the selected    constant radial temperature;-   means for calculating the mass flux from one finite volume to    another finite volume for the dielectric enhancement fluid component    within the finite volumes for the selected time period after the    initial time using the selected constant radial temperature;-   means for combining the calculated change in mass of the dielectric    enhancement fluid component within each finite volume with the    calculated mass flux between each adjacent finite volume for the    dielectric enhancement fluid component within the finite volumes for    the selected time period after the initial time to determine a new    concentration for the dielectric enhancement fluid component within    each finite volume;-   means for outputting the value of the new concentration for the    dielectric enhancement fluid component within each finite volume    using the selected constant radial temperature;-   means for using the outputted value of the new concentration for the    dielectric enhancement fluid component within each finite volume    using the selected constant radial temperature to determine the    second calculated concentration profile; and-   means for determining if the second calculated concentration profile    approximates the first calculated concentration profile, and if the    selected constant radial temperature does not result in the second    calculated concentration profile being determined to approximate the    first calculated concentration profile, selecting a new constant    radial temperature to use in determining the second calculated    concentration profile, and if the selected constant radial    temperature does result in the second calculated concentration    profile being determined to approximate the first calculated    concentration profile, using the selected constant radial    temperature as a flux-weighted temperature.

This computer simulation system can also include means for calculatingthe change in mass of the dielectric enhancement fluid component withineach finite volume due to chemical reactions for the selected timeperiod after the initial time using the selected constant radialtemperature, and means for combining the calculated change in mass ofthe dielectric enhancement fluid component within each finite volume dueto chemical reactions with the calculated mass flux between eachadjacent finite volume for the dielectric enhancement fluid componentwithin the finite volumes for the selected time period after the initialtime to determine a new concentration for the dielectric enhancementfluid component within each finite volume.

Also described is a computer-readable medium whose instructions cause acomputer system to simulate an electrical cable having a strandedconductor surrounded by a conductor shield encased in an insulationjacket and having an interstitial void volume in the region of theconductor injected with a fluid composition comprising at least onedielectric enhancement fluid component so as to at least partially fillthe interstitial void volume at an initial time, by performing variousones of the steps described above.

Other features and advantages of the invention will become apparent fromthe following detailed description, taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot of cable thermal classifications.

FIG. 2 is a schematic overview of the instant finite volume mass fluxcomputer simulation.

FIG. 3 is a finite volume representation of mass flux.

FIG. 4 is an illustration of the geometry of the innermost cable layerof a stranded conductor.

FIG. 5 is a plot of the temperature fluctuations typical of a heavilyloaded cable in a hyperthermic soil.

FIG. 6 is a plot of the radial concentration profile 5¼ years aftertreatment with a menthylanthranilate/ferrocene fluid mixture.

FIG. 7 is a plot of the cumulative exudation of the fluid mixture ofFIG. 6 from the insulation.

FIG. 8 is a plot of published data for OGE 15 kV 750 kcmil cable after14 months of field aging “Cable fault prevention using dielectricenhancement technology,” Mokry et al, Jicable 1995.

FIG. 9 is a plot of published data for Virginia Power energized butunloaded 35 kV, 1000 kcmil cable 15 months post-treatment “Cable faultprevention using dielectric enhancement technology,” Mokry et al,Jicable 1995.

FIG. 10 is a plot of published data for Virginia Power energized butunloaded 35 kV, 1000 kcmil cable 70 months post-treatment “FourthGeneration Dielectric Enhancement Technology,” Jenkins & Bertini,Jicable 1998.

FIG. 11 is a plot of Texas Utilities Field Failure from U.S. Pat. No.6,162,491.

FIG. 12 is a plot of the compilation of all available results of thepublished data according to FIGS. 8-11 showing the relationship betweenfluid concentration and post-treatment ACBD improvement.

FIG. 13 is a plot of siloxane concentration as a function of radialposition in a cable (digitized data from Kleyer & Chatterton).

FIG. 14 is a plot of the total fluid mass in the insulation as afunction of time (as reported by Kleyer & Chatterton).

DETAILED DESCRIPTION OF THE METHOD

The instant method relates to the restoration of an in-serviceelectrical power cable having a stranded conductor surrounded by aconductor shield encased in a polymeric insulation and having aninterstitial void volume in the region of the conductor, wherein adielectric enhancement fluid, or fluid composition, is injected into theinterstitial void volume. The instant method uses a computer simulationmethod to predict the concentration profile for each chemical species ofinterest present at a given time after injection. Chemical species ofinterest include water, all components which were originally present inthe injected dielectric enhancement fluid, and reaction productsthereof, including by-products such as methanol or ethanol (i.e.,byproducts of reaction of alkoxysilanes typically used in such cablerestoration with adventitious water). The concentration profile, inturn, can be used to predict the alternating current breakdown (ACBD)performance or reliability of a given cable after it is treated. Theinstant method employs a computer simulation, which provides thefollowing benefits and uses in five distinct modes:

R&D Mode

The performance of a dielectric enhancement fluid used to treat cablescan be predicted for various cable geometries and operating assumptionsknowing only the physical properties of the fluid. Formulationvariations can be virtually tested to optimize performance without theusual cost and time associated with electrical aging experiments.Contrary to the above described determination of treatment efficacy, theinstant simulation method requires only the gathering of variousphysical properties and employs a subsequent computer simulation topredict component performance, either alone or as part of a mixture.Such virtual experiments offer the benefit that many materials can betested and optimized before an actual fluid formulation is chosen.Additionally, this optimization can be performed at any granularity,from an individual cable to classes of cables.

Regime Delineation Mode

One shortcoming of previous art methods, such as those described in U.S.Pat. Nos. 5,372,840 and 5,372,841 which rely on diffusivity measurementsat 50° C., is the reliance on delineating certain classes of materialsby physical properties (particularly diffusion and equilibriumconcentration) at specific temperatures. Since cables operate at varioustemperature conditions depending upon, among other things, thetemperature of the soils in which they are buried and the cycling loadthey carry, using a single arbitrary temperature to delineate theproperties of materials is, at best, a compromise in precision and, atworst, an oversimplification which can distort reality to anunacceptable extent. To refine these classes, it is necessary toconsider more than a single temperature. Further, it is only possible toadequately delineate the classes of dielectric enhancement fluid to beused for very long-term performance improvement (e.g., the slow todiffuse fluids described in Publication No. US 2005/0189130 andPublication No. US 2005/0192708) by first using the instant computersimulation to provide a framework for the classification of materialproperties. While there are an infinite number of possible geometry andtime-dependent temperature profiles, the instant simulation allows thisto be reduced to a manageable number which covers the majority of realworld cases. The results of such simulations can then be used to selectthe types and amounts of dielectric enhancing fluid components which,when injected into an in-service cable, provide predictable dielectricbreakdown performance for decades under the given operating conditions.These general cases can then be used in R&D mode, above, to testspecific fluids within the case. In this mode, the simulation methodpermits one skilled in the art to reliably predict this performancewithout resorting to accelerated testing on actual cables, therebysaving both time and money. Moreover, while providing a goodapproximation of performance in view of the great complexity of thevariables involved, the instant simulation method is believed to besuperior to the current accelerated aging test method in predictinglong-term post-treatment field reliability. Furthermore, as the amountof data increases over time (particularly field performance data) thestatistical reliability of the instant simulation method willcorrespondingly improve.

Marketing Mode

The instant simulation method can be used to predict the reliabilityperformance of competitive products, thereby strengthening marketingposition of superior fluids and injection methods.

Pre-Injection Formulation Optimization Mode

With sufficient computer resources, it is possible to tailor individualformulations to customer requirements and cable conditions.

Post-Injection Performance Mode

After a cable is injected, its performance can be predicted whenunforeseen changes in the operation of the cable are required ordesired. As improved physical property data or improved theoretical ormore useful empirical relationships become available, the performancecan be reassessed to provide a refined reliable life estimate.

This allows the reassessment of anticipated performance in light of newinformation.

Granularity

As used herein, the term “in-service” refers to a cable which has beenunder electrical load and exposed to the elements, usually for anextended period (e.g., 10 to 40 years). In such a cable, the electricalintegrity of the cable insulation has generally deteriorated to someextent due to the formation of water or electrical trees, as well knownin the art. Further, the term cable “segment,” as used herein, refers tothe section of cable between two terminal connectors, while a cable“sub-segment” is defined as a physical length of uninterrupted (i.e.,uncut) cable extending between the two ends thereof. Thus, a cablesegment is identical with a sub-segment when no splices are presentbetween two connectors. Otherwise, a sub-segment can exist between aterminal connector and a splice connector or between two spliceconnectors, and a cable segment can comprise one or more sub-segments.The instant simulation method applies equally to a segment and asub-segment.

For each of the above five modes it is possible to use any level ofgranularity (i.e., the agglomeration of discrete cable lengths subjectedto the instant computer simulation as a single integral unit), from thatof an individual sub-segment of cable to entire classes of cables.Cables may be classified into groups by their geometry (i.e. conductorsize, conductor compression, thickness of polymeric layers, presence orabsence of an outer protective jacket, etc.), their materials (i.e.XLPE, HMWPE, EPR, etc.) and/or by their foreseeable dynamic temperatureprofiles. Consider the following examples which provide illustrations ofsome of the possible levels, from the smallest practical level ofgranularity to the greatest:

-   A 25-foot cable sub-segment which runs under an asphalt roadway. The    soil around the cable is warmer due to absorption of more solar    energy and hence the rate of fluid exudation from this sub-segment    is higher than for the rest of the segment.-   A single cable segment. While all the segments in a circuit are    electrically connected in an ostensibly series arrangement, load    decreases in segments which are remote from the source of power    because current is drained off from each transformer in the series    and from losses due to circuit impedance. Hence the cable nearest    the source caries the greatest load and the cable farthest from the    source carries the lowest load. A cable terminated on a stand-off    bushing at the loop normally-open point has no load. As a    consequence, the operating temperature of the remote segment is    likely lower than that of a segment close to the power source.-   3 segments of cable in a 3-phase circuit having a balanced load.-   A circuit (half loop or radial feed) wherein are all of the cables    have the same geometry and materials of construction.-   A class of cables which have generally the same geometry and    materials of construction and roughly the same thermal profile. One    such useful thermal classification system is illustrated in FIG. 1.

Thermal Classifications of Cable Operation

Over 90% of underground cables in the world are buried in soils whichhave mean annual temperature ranges that can be conveniently groupedinto the four soil regimes shown in the table below. It should be notedthat, although the cable depth is typically 1 meter, these soiltemperature regimes are defined by soil scientists at a depth of 0.5meter.

Cryic (or frigid) soil  0-10° C. Mesic soil  8-15° C. Thermic soil12-22° C. Hyperthermic soil 22-28° C.Further, many cables may be buried at depths other than 1 meter andcorrection to the temperature for such a cable depth may be required.That is, the soil temperature at cable depths other than 0.5 meters needto be corrected from the temperatures listed above and such correctionsare well known in the art. Moreover, cables buried in these variousthermal regimes can carry loads from zero (e.g., backup cables or radialfeeds far from the power source) up to the maximum design capacity ofthe cable. For most cables, the maximum conductor design temperature is90° C. but, for the purposes of the instant simulation method, it isuseful to consider three ranges of flux-weighted temperature (definedinfra) increase above the ambient soil temperatures, as follows:

lightly loaded <10° C. moderately loaded 10-20° C. heavily loaded >20°C.For the above four soil temperature regimes and three load conditionsthere would be 12 possible combinations, including some overlap, asshown schematically in FIG. 1. It would therefore be more convenient toformulate a smaller number of treatment regimes based on theflux-weighted temperature. For example, in FIG. 1, six formulations areselected, each formulation (numbered 10 to 60 at the right side of thisfigure) is a mixture including an extremely slow to diffuse component, amoderately diffusing component and, optionally, a fast to diffusecomponent which together in different ratios adequately covers thethermal ranges depicted in FIG. 1. Such specific catalyzed formulationsare illustrated in Table 1, below, wherein catalytic amounts oftetraisopropyl titanate (TIPT) are used in proportion to the totalamount of alkoxysilanes in a given formulation. In general, as thetemperature rises, the amount of slow flux components (i.e., lowdiffusion coefficients and/or low equilibrium concentration in the cableinsulation) is increased at the expense of the materials which exhibithigher flux, wherein “flux” refers to a radial mass transfer ratethrough the cable per unit length thereof.

TABLE 1 Formulation Number and Component Weight % Component 10 20 30 4050 60 acetophenone 18.00% 15.00% 12.00% 9.00% 6.00% 3.00%tolylethyl-methyl- 58.00% 53.00% 48.00% 43.00% 38.00% 33.00%dimethyloxysilane 2-cyanobutyl- 4.03% 12.00% 19.97% 27.94% 35.91% 43.88%methyl-dimethoxy- silane menthylanthranilate 0.64% 0.64% 0.64% 0.64%0.64% 0.64% avobenzone 2.40% 2.40% 2.40% 2.40% 2.40% 2.40% octocrylene9.60% 9.60% 9.60% 9.60% 9.60% 9.60% ferrocene 6.70% 6.70% 6.70% 6.70%6.70% 6.70% TIPT 0.63% 0.66% 0.69% 0.72% 0.75% 0.78% total 100.00%100.00% 100.00% 100.00% 100.00% 100.00%

The Instant Method Computer Simulation

FIG. 2 provides a schematic overview of a computational loop which isrepeated for each time increment, Δt, until the desired simulationperiod ends. Each box of FIG. 2 has a 3-digit code which relates to acorresponding section of this disclosure and a step in performing thecomputer simulation, below. Each section, in turn, provides an overviewof the calculations that are represented by the box.

In the simulation, finite volumes are defined by coaxial cylindersstretching the length of the simulated cable segment or sub-segment.(Note: The singular exception to this cylindrical geometry is theinnermost layer of the conductor shield which will be discussed indetail later and referred to as “layer zero” or Layer₀). Other than theinnermost volume, the finite volumes are in the shape of coaxial annularbands or layers, or as used herein annular cylinders or simply“cylinders”. Referring to FIG. 3, the cylinder corresponding toLayer_(I) is defined by an inner radius r_(I-1)and an outer radiusr_(I). As the number of layers or volume elements increases, theaccuracy and the precision both increase at the expense of thecomputational power required to perform the simulation. In practice, acompromise is made between simulation resolution and the length of timerequired to perform the simulation.

Section 000

This section of the simulation allows the user to provide physical andgeometric inputs to the simulation, including:

-   -   Time considerations, including the simulated length of the        simulation, the date and time for the start of the simulation,        the frequency at which data should be retained from the        simulation for post-simulation analysis.    -   The geometry and materials of construction of the cable    -   The electric field distribution of the cable in kV/mm across the        dielectric, which is easily calculated given the cable geometry        and the operating voltage in kV. The electrical field affects        the equilibrium concentration of polar materials in solid        dielectrics, as predicted by the Clausius-Clapeyron equation.        ([See Soma & Kuma, “Development of bow-tie tree inhibitor,” IEEE        1990.) The injection pressure, and where a soak is used, the        soak pressure and the soak duration.    -   The total quantity and composition of material supplied to the        interstitial void volume. Note that the total quantity can        generally be estimated from the actual pressure used and such an        estimate will generally suffice. However, when actual quantities        of fluid injected are measured, those measurements should be        utilized.    -   The physical properties of each component in the dielectric        enhancement fluid, along with water and products and by-products        of chemical reactions including:        -   Diffusion parameters, which allow the calculation of            coefficients within each layer of the cable, within the            temperature ranges of the simulation and within the            concentration ranges of the simulation.        -   Equilibrium concentration parameters of the components,            which allow the calculation of coefficients within each            layer of the cable, within the temperature ranges of the            simulation, within the concentration ranges of the            simulation, including binary interactions between            components, and within any dielectric layers wherein the            equilibrium concentration is influenced by an AC electrical            field (i.e., equilibrium concentration for any molecule with            a non-zero dipole moment).        -   Molecular weight of the components (needed for chemical            reaction molar balance calculations)        -   Density of the components (needed to calculate pressure in            the interstitial void volume of the cable).    -   The approximate seasonal water concentration in the soil is        generally obtained from historical data. These historical-based        predictions can be refined by climate modeling and micro-climate        modeling when the cable transfers substantial energy into the        soil. The U.S. Department of Agriculture provides this kind of        data at their web site. Ampacity calculations take the water        content of the soil into account for accurate predictions as the        water content has a significant effect on soil thermal        conductivity.    -   Chemical reaction parameters including:        -   Identification of the stoichiometry of all significant            chemical reactions, including those involving any catalyst            incorporated        -   Reaction rate parameters            -   Frequency factor            -   Activation energy    -   The void volume distribution or “halo” (further described below)        within the dielectric layer of the cable. The halo can be        measured by saturating a cable sample with a fluid and        quantifying the concentration profile of the fluid across the        radius of the insulation. The profile (i.e., a value over a        distance (radius)) of the total water concentration minus the        equilibrium water concentration in un-haloed polymer divided by        the water density yields the halo profile (the profile is        measured experimentally or generalized from data available in        the literature).

Section 050

In this section, parameters which affect the operating temperature ofthe cable are entered. The user must provide temperature and thermalproperty inputs, each as a function of time over the lifetime of thesimulation. At a minimum these inputs include the load in amperes, thesoil temperature at cable depth (away from the heating influence of thecable), and the thermal conductivity of the soil. Examples of additionalvariables which may influence results and may be included as refinementswhere the effects are significant, include local conditions such as: 1)the layout of multi-phase circuits where the heat output of individualcables impacts the temperature of the soil surrounding adjacent cables,and 2) other sources of heat such as buried steam pipes. These inputsare used, along with the cable geometry and cable materials ofconstruction, to provide the temperature at any radius (r) within thecable profile and at any time (t) over the anticipated post-treatmentlife using methods well known in the art. This section is only for inputcalculations, and temperature distribution calculations will bediscussed in Section 100 below.

Section 100

Using the parameters entered in Section 000 and 050, this sectioncalculates the dynamic radial temperature profile for each finite volumelayer. If it is desired to model a specific case, then the radialtemperature profile as a function of time is available from finiteelement calculations, such as those described in Section 050, above, orcalculated by software available from CYME International. Alternatively,since it makes little sense to employ computationally intensive finiteelement modeling methods to model general cases, a simplified model oftemperature fluctuations may be used as a representation of generalcases. FIG. 5 is just such a representation of a typical heavily loadedcable in a hyperthermic soil. A specific case would include plannedloading profiles, for example a feed to a chemical plant might have analmost constant load, except during the annual 2 week maintenanceshut-down. This is differentiated from a general case which exhibits atypical and generally sinusoidal temperature profile, as shown in FIG.5.

Section 200

Using the parameters entered in Section 000 and 050 and the calculationsin Section 100 and the conditions from the previous iteration of theloop, this section:

-   -   Calculates the collective values solute mass and total mass for        each finite volume layer by summing the mass of each component        of the dielectric enhancement material.    -   Calculates the approximate interstitial volume actually filled        with material by dividing the total mass of material in the        interstices by the sum of the products of each component density        and its respective mass fraction.    -   Calculates the concentration of each component of the fluid in        terms of mass per unit volume.    -   Calculates the pressure of the remaining mass in the interstices        as the various components of the dielectric enhancement fluid        diffuse into the insulation jacket where there is no soak bottle        attached to the cable. A good approximation can be obtained with        a linear pressure decrease from the initial pressure to zero as        the mass decreases from its original mass to the mass which can        fit without any pressure in the interstitial space.    -   Determines whether the pressure in the interstices is        sufficiently high that a “layer zero” (See Layer₀ in FIG. 4)        zero-by-pass condition exists (i.e. the pressure is high enough        that fluid flows along the outer circumference of the outer        strands and effectively can permeate directly into Layer₁).        Layer zero is the portion of the conductor shield which is        extruded between the outermost strands of the conductor strand        bundle. When interstitial pressures are low, there is a        bottleneck in mass flux between the interstices and all layers        of the polymer from Layer₀ outward. This limited area,        represented in one dimension by the smallest arc in FIG. 4 and        in the other dimension by the length of the cable under        consideration, is a tiny fraction of the area represented by the        largest arc and the same cable length, which would be available        for diffusion if Layer₀ were bypassed. The ratio (small to        large) of these two areas is the L₀ restriction.

Section 300

Using the parameters entered in Section 000 and 050 and the calculationsfrom 100 and 200, this section:

-   -   Calculates the change in mass resulting from all significant        chemical reactions, including the parallel reaction routes which        result from the presence of catalysts, for each finite volume        element and for each component of the dielectric enhancement        fluid.    -   Converts all concentrations to molar concentrations        (g-moles/cm³). For a typical hydrolysis or condensation reaction        of A+B+C→D, the rate equation is

−r _(A) =kC _(A) C _(B) C _(C)

wherein C_(A), C_(B), C_(C) denote the molar concentrations ofcomponents A and B and catalyst C, respectively, k is a rate constantand r_(A) is rate of the reaction of component A. The rate constant is,in turn, a function of temperature:

k=k ₀ e ^(−E/RT)

where k₀ is the frequency factor, E is the activation energy, R is theideal gas constant, and T is the absolute temperature. The chemicalreaction rate equations for each reactive component are solvedsimultaneously and the form of the equation may vary from the aboveexample. Not to be confused with the ideal gas constant R justdescribed, ΔR_(i,I) is the net change in mass of each component, i,within each finite volume element, I. This net change in mass fromchemical reaction is next used in Section 800, as described below.

Section 400

Using the parameters from 000 and 050 and the calculations from Section100 and 200, this section calculates the equilibrium concentrationprofile for each component of the dielectric enhancement fluid withineach layer at the given simulation time. The equilibrium concentrationsare determined in three steps and incorporate the followingconsiderations: (1) pure component equilibrium concentration, includingthe effect of the electrical field, as predicted by theClausius-Clapeyron equation of phase transition, (2) effect of componentinteractions, and (3) the effect of the halo within the insulation.

Pure Component Equilibrium Concentration

Utilizing an Arrhenius exponential function, or any empirical functionthat has been fitted to the data over the temperature range of interest,the pure component equilibrium concentration, Ci, as a function oftemperature for each component and in each finite volume element, isdetermined. Not only does the pure component equilibrium concentrationvary with temperature, but it varies with the composition of thematerial of the respective finite volume. Thus, separate functions arerequired for each of the following layers, if present, in the cableconstruction: conductor shield, insulation jacket, insulation shield,and jacket material(s). The only layer that supports a significantelectrical field is the insulation layer and an adjustment to the purecomponent equilibrium concentration should be made. This adjustment canbe accomplished either with experimental measurements fitted to anempirical function or, where relative permittivity values of thecomponent in the liquid and vapor phases and the permittivity of theinsulation are known, the Clausius-Clapeyron formula can be used toprovide estimated adjustments. The solubility increases for high DKmaterials in higher electrical fields are shown by Soma & Kuma,“Development of bow-tie tree inhibitor,” IEEE 1990]

Component Equilibrium Concentration with Component Interactions

The equilibrium concentration of any individual component in a polymerphase is impacted by the presence of other components dissolved in thepolymer phase. A variety of mathematical methods may be utilized tomodel the component interactions. One useful model is provided below toillustrate the concept. The component (i) equilibrium concentration,which is adjusted for the presence of other components, is denoted byC′_(i). For the interstices, there is no interaction with a polymer, soC′_(i) equals C_(i). For all polymeric or rubber layers:

$C_{i,l}^{\prime} = {{C_{i,l} \cdot \frac{m_{i,l}\left( {{{{for}\mspace{14mu} {component}\mspace{14mu} i}\&}\mspace{14mu} {layer}\mspace{14mu} l} \right)}{\Sigma \; {m_{i,l}\left( {{{{for}\mspace{14mu} {all}\mspace{14mu} {components}\mspace{14mu} i}\&}\mspace{14mu} {layer}\mspace{14mu} l} \right)}}}\alpha_{i}}$

wherein m is the mass in grams and alpha (α_(i)) is an empiricalcoefficient having a value between 0 and 1 which models the departurefrom ideal solution behavior. This empirical coefficient can bedetermined experimentally in at least two ways. In the first,experimental data, as described below in “Example of the instantsimulation method in a

Marketing Mode,” is utilized to adjust the α_(i) function to fit datasuch as those shown in FIG. 9. In the second, polymer slabs can beexposed to known quantities of material pairs. The slabs can besacrificed and the concentration of the binary pairs can be quantified.With all values directly measurable except α_(i), the latter constantcan be calculated directly for the component pair. For the materials andtemperature ranges of interest, the total component equilibriumconcentration in any polymer layer remains relatively low (i.e., thetotal concentration is typically below 0.1 g/cm³). For most systems, theinteractions of component pairs in such dilute polymer solutions can beadequately modeled using only the binary interactions of solutecomponents. The dilute nature of the solution allows tertiary and higherinteractions to be ignored without significant impact on the accuracy ofthe calculations. However, where higher-order interactions aresignificant, they can likewise be measured, albeit with a large numberof experiments.

Component Equilibrium Concentration with Fluid Interactions Plus Halo inInsulation

A halo is a dispersion of micro voids in the dielectric material (i.e.,the insulation) and is generally caused by repeated thermal cyclingwhile the material is saturated with water. Current in a cable generallycycles over a 24 hour period between maximum and minimum values. As aconsequence, the temperature of the cable cycles with the samefrequency. The equilibrium concentration of water in the dielectric is astrong function of temperature and, as the temperature increases, morewater permeates into the cable. As the temperature decreases, the waterattempts to retreat from the cable, but it cannot do so fast enough toavoid supersaturation, particularly near the middle of the insulationlayer. The water condenses out of the polymer phase and formswater-filled micro voids. The volume of halo micro voids in each finitevolume element, H_(I), forms an approximately normal distribution whichcan be fit to comport with measured values obtained with a microinfrared scan of the wet insulation or a Karl-Fischer titration thereof.Each component of the dielectric enhancement materials, water and anyproducts or by-products of their chemical reactions in the void volumeof the halo is in dynamic equilibrium with the same component in thepolymer matrix. The component distribution in the halo is proportionalto the actual amount of component in the finite volume element and theequilibrium concentrations of those components in the finite volumeelement. The halo adjusted equilibrium concentration, C″_(i,I) is:

C″ _(i,I) =C′ _(i,I) +H _(I) [ω·C′ _(i,I) /ΣC′ _(i,I)+(1−ω)·m _(i,I) /Σm_(i,I)]

wherein ω (omega) is an empirical weighting factor with a value between0 and 1 which is adjusted to fit experimental data of the type providedin FIGS. 8 and 9.

Section 500

Using the parameters input in Sections 000 and 050 and the calculationsfrom Sections 100, 200, and 400, this section calculates the diffusioncoefficient profile, D_(i,I), of each component, i, and for each finitevolume layer, I, as a function of temperature and concentration. Thereare a number of suitable empirical relationships to accommodate thetemperature and concentration dependence of diffusion, the equationbelow being illustrative:

−Q _(i) /T _(I) ξ_(i) ·ΣX _(i,I) D _(i,I) =A _(i)·10·e

wherein A_(i) and Q_(i) are empirical constants for component (i) whichreflect the change in diffusion with temperature at infinite dilution,ξ_(i) is an empirical constant for component i which reflects theconcentration dependence, ΣX_(i,I) is the concentration of all solutecomponents (i=1−n, where n is the number of solutes) in element I, andT_(I) is the absolute temperature of finite element, I. There are a widevariety of methods well known in the art to gather diffusion data atvarious temperatures and concentrations which can then be fitted to theabove equation using a least-squares or similar regression approach. Onemethod often employed is to immerse a slab sample of polymer in thefluid of interest at a constant temperature. The slab is periodicallyremoved from the fluid and weighed to generate a curve of weight gainversus time. Using the formulae and method described in EngineeringDesign for Plastics, 1964, edited by Eric Baer, Chapter 9: Permeabilityand Chemical Resistance, equation (26) on page 616 provides that thediffusion coefficient as a function of time (t) to half saturation is:Thus, this section calculates a new D for each layer, I, and eachdelta-t,

D=0.04939/(t/λ ²)_(1/2).

where λ is the slab sample thickness and the subscript designates thehalf-saturation condition.

Section 600

Using the parameters of Sections 000 and 050 and the calculations fromSections 100, 200, 400, and 500, this section calculates the lag time,t_(lag,i,I), defined herein as the time it takes a molecule of acomponent to traverse the thickness of a given cylindrical layer, foreach component, i, and each finite volume element, I, as described inCrank & Park, Diffusion in Polymers, p. 177 (1968), equation for “A.”This expression applies to a cylinder having a single homogenouscomposition, as is the case for each finite volume element of theinstant simulation method.

t _(lag,i,I)=[(r _(I) ² +r _(I−1) ²)·In(r _(I) /r _(I−1) ²)−(r _(I) ² −r_(I−1) ²)]÷4D _(i,I) ·In(r _(I) /r _(I−1))

Section 700

Using the parameters of Sections 000 and 050 and the calculations fromSections 100, 200, 499, 500, and 600, this section calculates the massflux (ΔM_(i,I)) for each component, i, and between each finite volumeelement, I, when

${\sum\limits_{l = 0}^{l}t_{{lag},i,l}} > t$

where t is the cumulative elapsed simulated time, and t_(lag,i,I) is thetime lag for each component, i, and within each finite volume element,I. Permeation between adjacent finite element layers can only occurwhere the sum of the time lag values for each component from finitevolume element 0 (zero), to the outermost of the two finite volumeelements, I, is greater than the elapsed simulation time, t. When thelag time constraint is satisfied,

ΔM _(i,I)=2π L D _(i,I)·Δμ_(I) ·Δt·In(r _(I)/r_(I−1))

where Δμ_(I) is the potential gradient in mass per unit volume, asdescribed below, between layers I and I−1, L is the length of the cablesegment or sub-segment and Δt is the time increment for this simulationiteration loop. The potential gradient between two adjacent finitevolume elements, Δμ_(I), can be approximated more than one way. Anexample of one approximation is provided below to illustrate theconcept.For cases where X_(i,I)/C′_(i,I)>X_(i,I+1)/C′_(i,I+1)

Δμ_(I) =X _(i,I+1) −C′ _(i,I+1) ·X _(i,I) /C′ _(i,I)

and where X_(i,I)/C′_(i,I)<X_(i,I+1)/C′_(i,I+1)

Δμ_(I) =−X _(i,I) +C′ _(i,I) ·X _(i,I+1) /C′ _(i,I+1)

It should be noted that, within the insulation layer, C″, whichaccommodates the halo, is substituted for equilibrium concentration C′in the four expressions above and the other symbols have their previousdefinitions.

Section 800

Using the parameters of Sections 000 and 050 and calculations fromSections 100, 200, 300, 400, 500, 600, and 700, this section sums theabsolute mass of the previous iteration (M_(i,I)(t−Δt)) for eachcomponent, i, in each finite volume element or layer, I, with the massflux (ΔM_(i,I)) into and out of each finite volume element and the netchemical reaction, ΔR_(i,I) to yield the new absolute mass, M_(i,I)(t).

M _(i,I)(t)=M _(i,I)(t−Δt)+ΔM _(i,I−1) −ΔM _(i,I) +ΔR _(i,I)

where M_(i,I)(t) represents absolute mass, t is the current elapsedsimulation time, (t−Δt) is the elapsed simulation time of the previousiteration, and all of the “delta” terms represent the respectivevariable changes calculated over the increment Δt.

Sections 900-950

These sections control program output to a display screen as well asfiles and program termination when the simulation is completed.

Section 975

This section calculates the Δt for the next iteration. In practice, thedynamics (i.e. the lag times for the fastest to diffuse components whichwere calculated in Section 600) of the previous iteration are used tooptimize the Δt. From trial and error experience, a factor (this lagtime multiplication factor may generally be as high as 3 to 10) ismultiplied by the smallest lag time of the previous iteration toestablish a new Δt. Too large a Δt causes the calculation to becomeunstable and potentially fail; too small a Δt while increasing accuracyand numerical stability, uses greater computational resources. Generallythe most dynamic element will establish the required Δt (i.e. the mostdynamic element has the minimum Δt). To reduce the number of requiredcalculations and to enjoy the economy of rapid computations, wholenumber factors can be established between the most dynamic element (veryoften the diffusion of water) and at least one, or even more preferably,most of the less dynamic elements. For example, if the calculated lagtime for the diffusion of water in one finite element was 3 seconds andthe lag time for a particular chemical reaction was 61 seconds, a wholenumber factor such as 20 (61÷3, rounded to a whole number) could beassigned to the chemical reaction such that the reaction equations aresolved once every 20 iterations.

Section 999

This section increments the time, t by Δt and begins another iterationloop at Section 100.

Examples

The various utilities (modes) of the above described simulation will nowbe illustrated by way of non-limiting examples to further clarify thedifferent embodiments of the instant simulation method.

Example of the Instant Simulation Method in a Regime Delineation Mode

In the following example an embodiment of the instant simulation methodis illustrated wherein the computer simulation is utilized to providethe distribution of fluid components in a cable and facilitateconvenient grouping of commonly occurring cases of similar conditions,as illustrated in FIG. 1. This grouping of similar situations avoids theimpracticality of dealing with the vast number of possibilitiesindividually.

For illustrative purposes, consider a typical cable segment carrying aheavy current load in a hyperthermic soil which experiences thetemperature fluctuations depicted in FIG. 5. The seasonal fluctuation ofthe bulk soil temperature is shown by the lower dashed sinusoidal curveas a function of time in months (ranging from 0 to 12 months on thex-axis). The upper 12 sinusoidal curves indicate the daily (0-24 hourson the x-axis) average fluctuations in conductor temperature for each ofthe 12 months of the year. The solid monotonically declining linedescribes the radial temperature profile across the cable conductorshield, insulation, and insulation shield at a particular simulatedmoment (e.g., 3:45 PM on Aug. 31, 2010), the corresponding abscissabeing scaled such that zero represents the innermost radius of theconductor shield and 24 represents the outermost radius of theinsulation shield. It is further assumed that the above cable segment is220 feet long and is of the following construction: unjacketed; 15 kV,100% insulation (180 mil); 1/0, 19-strand, aluminum concentricconductor. The cable is injected (virtually) at time t=0 (e.g., noon;Jun. 2, 2005) with 839 grams of a two-component dielectric enhancementfluid mixture consisting essentially of 755 grams of menthylanthranilateand 84 grams of ferrocene. The mass of fluid supplied is the mass whichwould be supplied and confined at a pressure of 100 psig according tothe method described in Publication No. US 2005/0189130, cited above.

From the computer simulation described above, the approximate radialconcentration distribution of each component of the above fluid mixture,as well as the total thereof, is provided in FIG. 6 for a time t=5¼years after the virtual injection. In this figure, the respectivecomponent weight percentage is plotted against radial position in thecable and each interface between the various layers of the cable isdelineated with a vertical demarcation line. Thus, working from left toright, the first interface is between the stranded conductor and theconductor shield, then between the conductor shield and the insulation,then between the insulation and the insulation shield, and, finally,between the insulation shield and the hyperthermic soil in which thecable is buried. The curve for each component of FIG. 6, which is anoutput provided in Section 910 of the above simulation, can benumerically integrated with respect to radial position out to theoutermost layer of the insulation and results then summed and finallysubtracted from the initial total amount of fluid injected at t=0 toprovide the total amount of fluid which has exuded from the cable at theabove simulation time. Thus, for example, according to the computationof this simulation at 5¼ years after virtual injection (treatment), overhalf of the fluid supplied has exuded from the insulation. Thecumulative exudation at various times is, in turn, plotted in FIG. 7 asthe data points labeled “Hyperthermic; heavy load”. Plotted alongsidethe data for the above example cable, which shows the respective pointsfor simulations up to year 10 after virtual injection, are a series ofassumed isothermal simulations between 27.5° C. and 50° C. (i.e., thetemperature of the cable and the soil are assumed to be constantthroughout each simulation), as indicated in the legend of FIG. 7. Theassumed isothermal temperature of each subsequent simulation is chosenwith the objective of matching the value of the virtual exudation curveat the end point of interest. For example, if the customer specifiedreliability requirement, as defined infra, is 10 years after actualtreatment, the isothermal temperature which best matches the exudationcurve at 10 years after virtual injection lies between 45 and 46° C.This isothermal temperature which most closely matches the exudationrate profile of the field cable at the customer specified design life isdefined herein as the “flux-weighted temperature” according to theinstant simulation method. For this example, with a customer specifiedreliability requirement corresponding to about an 80% exudation level(i.e., 80 wt % of the total fluid introduced is predicted to exuded fromthe insulation after 10 years), that temperature is approximately 45.3°C. and the 45.3° C. isothermal exudation line would cross the“Hyperthermic; heavy load” line at about post-treatment year 10.

In practice, of course, cable owners would not specify the abovementioned exudation value. Instead, they specify a dielectricreliability requirement. Thus, the cable owner can predict theapproximate AC breakdown value of particular circuits utilizing at leastone of several known methods:

-   -   Operational reliability history of the circuit, adjacent        circuits, or similar circuits is predictive.    -   Samples of a population of cables can be excavated, analyzed,        and assumptions about the performance of the population can be        inferred.    -   Diagnostic tests, such as partial discharge or isothermal        relaxation current, provide approximations of cable reliability        performance.

Furthermore, it is well known in the art what AC breakdown performanceis required to provide a desired level of reliability. One usefulbenchmark is that of Steennis (E. Frederick Steenis, “Water treeing: thebehavior of water trees in extruded cable insulation”, KEMA, 2^(nd)edition 1989). After extensive testing and comparison to operationalreliability, it was found that, within the population of the cablestested which exhibited AC breakdown performance above 16 kV/mm (63%probability), none had ever failed in service. Thus, a customer mightspecify AC breakdown performance of 18 kV/mm for circuits with very highreliability requirements (e.g., hospitals, military facilities,electronic media broadcasters, emergency responder facilities, andmanufacturing facilities) and perhaps a lower value such as 16 kV/mm forcircuits that feed less critical applications, such as residentialneighborhoods.

Using data published in the literature it is possible to makepredictions of post-treatment reliability based upon the concentrationof treatment fluids in the insulation. FIGS. 8, 9, 10 and 11 arepublished results which disclose both the actual AC breakdownperformance and the concentration profiles of the treatment fluid in theinsulation. These figures represent different cables which were treatedin the field with CableCURE®/XL fluid, the latter being a catalyzedmixture comprising phenylmethyldimethoxysilane andtrimethylmethoxysilane in an approximately 70/30 weight ratio andmarketed by Utilx Corp. As described previously, the concentrationprofiles in FIGS. 8 to 11 are numerically integrated to obtain the totalfluid within the insulation. FIG. 12 is a compilation and transformationof these numerical integrations wherein the solid curve represents aregression fit of the points. Furthermore, for the data presented inFIG. 12, pre-treatment AC breakdown results, post-treatment AC breakdownresults, and the concentrations of treatment fluids are published oreasily estimated. By definition, the origin in FIG. 12 (i.e., 0,0 point)is known for each of these cases. That is, the increase in AC breakdownperformance is zero at time zero. The post treatment ACBD data istransformed into the “percent recovered” metric of FIG. 12 as follows:

% ΔACBD _(recovery)=(ACBD _(post treatment) −ACBD_(pre-treatment))÷(ACBD _(new) −ACBD _(pre-treatment))

where ΔACBD_(new) is arbitrarily defined as 40 kV/mm for polyethylene(PE) and 31.5 kV/mm for EPR-insulated cables, these values being typicalfor the respective polymers. Other values may be used for otherinsulation systems. In addition to the data of FIG. 12, a polynomialmodel is available to show the general relationship, at least for thepreferred embodiment of the fluid mixture discussed in U.S. Pat. No.5,372,841. It is believed that performance of other fluids would likelyfollow different lines than that shown in FIG. 12. The above polynomialmodel of FIG. 12 is represented by the equation:

% ΔACBD=a ΣX _(i) ^(b) −c(Σx _(i) −d)²

where a, b, c, and d are constants determined by statistical means, ΣXiis the sum of the individual concentrations of the alkoxysilane andsiloxane oligomers of the CableCURE/XL fluid, and where the second termis 0 (below the threshold value of “d” for all negative (ΣXi−d) (i.e.,the data is fit empirically to this mode and the second term has a floorvalue of zero. The curve in FIG. 12 is defined by the foregoing equationand values for a, b, c, and d of 3.5, 0.5, 1800, and 0.3, respectively,obtained from a computer fit of the data. The first term (aΣxib) definesa generally parabolic relationship with diminishing returns of ACbreakdown recovery for increasing concentration of treatment fluids. Thecompeting second parabolic term (−c(Σxi−d)2) represents mechanicalstrains from swell which subtract from cable reliability. This oversaturation (or swelling), and the resulting strains, is induced in thecable by ever increasing concentrations of treatment fluid. “Oversaturation” is defined herein as the introduction and dissolution of arelatively soluble component (e.g., one having a solubility in theinsulation of greater than about 3 weight % at cable operatingtemperatures) which can lead to excessive swelling of the insulation andresult in degradation of the mechanical properties thereof. Until somethreshold concentration (d) is met, the second term is ignored, but onceΣXi exceeds (d), the function is evaluated and further increases inconcentration decrease the reliability of the cable (i.e., a transitionto over saturation occurs). A further effect of over saturation can beseen in FIG. 12, wherein a concentration of fluid greater than about0.03 g/cm 3 is associated with reduced ACBD performance. Additionally,over saturation with any individual component can result in interferencewith the diffusion/equilibrium concentration of the other components inthe insulation. This is in contrast with supersaturation, which is thecondensation of previously dissolved fluid from the insulation due tothermal cycling, as described in U.S. Pat. No. 6,162,491, which teachesthat the equilibrium concentration of the total amount of solublecomponents should be reduced by dilution to avoid supersaturation. FIG.11 is a re-plotting of the data of FIG. 2 in U.S. Pat. No. 6,162,491.Swelling approaching 9% provides, and the attendant decrease inreliability demonstrates, that there is a point where too much fluid canbe supplied to inflict damage from over saturation. However, it is nowbelieved that a better approach to avoid supersaturation is the use ofcomponents having flat equilibrium concentration-temperature profiles.The instant simulation method, together with post-injection performancemodels compiled using experimental data, can thus be used to estimatepost-injection reliability.

With an approximation of the existing performance and the desiredreliability specification, a correlation such as that depicted by FIG.12 is applied to determine the minimum concentration of treatment fluidrequired to meet the reliability requirement. For example, referring toFIG. 12, assume a cable has an estimated 40 kV/mm original AC breakdown,with an estimated 10 kV/mm remaining AC breakdown (see above mentionedestimation methods), and it is desired to have an 18 kV/mmpost-treatment AC breakdown. Then, from FIG. 12, the fluid concentrationin the insulation must be maintained above 0.0056 g/cm3 (i.e., the pointwhere the simulation line, labeled “SiLDK model” in FIG. 12, crosses 27%“Post-treatment ΔAC BD Recovery” on the way up, where the 27% ΔAC BD isthe change in AC BD=100 (18−10)/(40−10), but not greater than 0.0475g/cm3 (i.e., the point where the “SiLDK model” line crosses 27% on the“Post-treatment ΔAC BD Recovery” on the way down) to avoid oversaturation, as defined herein. Again, it should be recognized that theregression line of FIG. 14 must go through the origin (0, 0) since theconcentration of treatment fluid is necessarily zero when fluid is firstfed into the cable. The fluid concentration increases over time to somemaximum and then begins a general decline, which may be punctuated withlocal maxima. Further restricting the shape of the time-dependentconcentration curve of FIG. 14 is the requirement that the curve muststart at zero and end at zero and can never be negative. How quickly thefluid concentration crosses the minimum performance expectation on theway up is also important and it is also predicted by the instantsimulation method. When a high pressure method, such as that describedin above cited Publication No. US 2005/0189130 or Publication No. US2005/0192708 is used to inject and confine the dielectric enhancementfluid in a cable, this time can be a matter of several days. However,with the prior art (low pressure) approaches, months or even years canpass before the maximum performance is achieved and the instantsimulation method allows prediction of dielectric performance for a widevariety of circumstances as a function of time. A plot similar to thatof FIG. 12 can be obtained for any other restorative fluid composition,such as the above described mixture of menthylanthranilate and ferroceneor the compositions of Table 1, and the above description will serve toillustrate its application in the practice of the instant simulationmethod.

Again, for the above discussed menthylanthranilate/ferrocene mixture,integration of each component curve within the insulation area of FIG. 6with respect to radius, in the manner discussed above, yields a totalpredicted treatment concentration of 0.0143 g/cm³ after 5¼ years. If,for example, the menthylanthranilate/ferrocene system had a similarperformance profile to the SiLDK model of FIG. 12, the treatment wouldprovide more than the above required minimum treatment fluidconcentration of 0.0056 g/cm³. The simulation is continued until thetotal fluid concentration is predicted to reach a value equal to thecustomer specified minimum (e.g., 0.0056 g/cm³ in the above example). Itis at that point that the time and exudation indicated in FIG. 7 isestablished and at which an isothermal simulation curve crossessimulated data to establish the flux-weighted temperature (e.g., 80%exudate after 10 years in FIG. 7 in the above example).

Optimization of performance can be made at one flux-weighted temperaturewhich matches several of the field profiles plotted in FIG. 1. Each ofthe formulations listed in Table 1 represents just such an optimization.Furthermore, once the flux-weighted temperature is determined accordingto the above described simulation, preferred components can beidentified and included in the dielectric enhancement fluid compositionused to treat the subject cable, employing either a conventionallow-pressure method or a high-pressure one, as disclosed in PublicationNo. US 2005/0189130, cited supra. Again, each fluid described in Table 1includes some of these preferred components.

Since increasing the amount of fluid injected increases the amount oftime each component thereof is present above any threshold concentrationand needed to provide the desired ACBD value, the amount of total fluidpreferably injected is as large as possible. This preferably entailsusing the above mentioned high-pressure method, but can be used with thelower pressure methods as well, in either case with the followingpreferred constraints:

-   -   1. The pressure of injection and containment should be below the        yield point of the cable,    -   2. Total fluid within the insulation at any time during the        post-treatment period is maintained below the point where over        saturation hampers reliability performance,    -   3. Treated life expectancy of the cable meets or exceeds        customer requirements, and    -   4. The incremental cost of additional fluid (and/or its        delivery) is greater than the value perceived by the customer.

Example of the Instant Simulation Method in a Marketing Mode

The following example illustrates that the prior art method usingphenylmethyldimethoxysilane or CableCURE® with a low pressure injectionusing a soak period is predicted by the simulation to have inferiorlongevity versus one of the formulations of Table 1.

Consider the cable described by Kleyer and Chatterton in their paper,“The Importance of Diffusion and Water Scavenging in DielectricEnhancement of Aged Medium Voltage Cables” (IEEE/PES conference; Apr.10-15, 1994). The cable and the experiment were described as follows:

-   -   “ . . . a 1/0 AWG, 15 kV rated cable . . . cut into segments,        filled with phenylmethyldimethoxysilane and the ends sealed        before immediate immersion in a 60° C. constant temperature        water bath. At various time intervals (7, 17, 27, 54, 67 and 248        days) a segment was removed from the bath, sectioned and the        insulation was profiled by microscopic infrared spectroscopy for        treatment distribution.”

The results of that experiment, which are plotted in FIG. 4 in theKleyer & Chatterton paper, were refined and re-plotted in “DielectricEnhancement Technology” by Bertini & Chatterton in March/April 1994 IEEEElectrical Insulation Magazine. The latter data were digitized and arere-plotted herein in FIG. 13. It should, however, be noted that theoriginal paper by Kleyer and Chatterton did not provide a completedescription as the insulation thickness was omitted and the abovementioned refinement required some assumptions/approximations.Nevertheless, this should serve to illustrate the principles of theinstant simulation method and a similar plot for any given fluid couldbe generated and used to fit the parameters, as described below.

The total amount of fluid in the insulation of the cable for each curvein FIG. 13 (M_(insulation)) can be obtained by numerically integratingthe concentration profile across the cylindrical geometry of the cable:

M _(insulation) =Σ X _(siloxane,I) ·v _(I) (for all layers, I, providedin FIG. 13)

where X_(siloxane,I) is the mass concentration of the silane monomer andits siloxane oligomer components (in this case,phenylmethyldimethoxysilane and oligomers thereof and having the unitsg/cm³) in each layer, I. In the above equation, v_(I) is the volume ofeach cylinder, defined by an arbitrary length and inner and outer radii.The mass concentration is the measured value halfway between the innerand outer radii. The results of this calculation are shown as trianglesin FIG. 14 and reveal the total concentration of silane and siloxane inthe insulation for the following times: 7, 17, 27, 54, 67 and 248 days.Plotted along with the above data in FIG. 14, are simulations (i.e., thecurves) according to the instant method, wherein the above mentionedparameters were adjusted until an acceptable regression fit was achieved(Sim 36 in FIG. 14). Notwithstanding the necessary approximation of theabove data refinement, and deciphering the cable geometry as best aspossible, it is possible to virtually recreate the 12 year-oldexperiment using the instant simulation and derive information aboutreaction rates and permeation properties of thephenylmethyldimethoxysilane fluid. Thus, the parameters that areadjusted to fit the data of FIG. 14 are:

-   1) Reaction rate,-   2) (α) for the phenylmethyldimethoxysilane and its oligomers and (α)    for water,-   3) amount of initial fluid as a percentage of the interstitial    volume,-   4) layer zero restriction ratio, and-   5) extent and location of the halo as a histogram, wherein the halo    is the percent of the insulation volume that is void (i.e. no    insulation). The histogram may often be conveniently represented as    a normal distribution by identifying the radial location of the    peak, the value of the peak and the standard deviation of the    distribution along the radius.

A computer program could employ well-known techniques, such as anadaptive randomly directed search, to adjust all of the above parameterssimultaneously to get the best fit to a plot like FIG. 14.Alternatively, these parameters could be adjusted one at a time, or afew at a time. Utilizing standard regression procedures one candetermine the best fit solution for the parameters. As an example, theactual parameter values obtained in Simulation 36 (Sim 36) in FIG. 14are:

-   (1) Reaction rates:

The following table summarizes the various parameters for rateconstants, k, for phenylmethyldimethoxysilane and its products ofhydrolysis/condensation.

with titanium(IV) without catalyst isopropoxide catalyst FrequencyFrequency Factor Activation Factor Activation k₀ energy E k₀ energy EReaction (mol/cm³)^(1-n)/sec cal (mol/cm³)^(1-n)/sec cal PhMe-1.0 + H₂O→ PhMe-1.1 + MeOH 5.67E+14 23,000 5.67E+14 10,000 PhMe-1.1 + H₂O →PhMe-1.2 + MeOH 2.83E+14 23,000 2.83E+14 10,000 2 PhMe-1.1 → PhMe-2.0 +H2O 1.42E+14 23,000 1.42E+14 10,000 2 PhMe-1.1 → PhMe-2.1 + MeOH1.42E+13 23,000 1.42E+13 10,000 2 PhMe-1.2 → PhMe-2.2 + H₂O 2.83E+1423,000 2.83E+14 10,000 PhMe-1.1 + PhMe-1.0 → PhMe-2.0 + 7.08E+12 23,0007.08E+12 10,000 MeOH PhMe-1.1 + PhMe-1.2 → PhMe-2.1 + H₂O 1.89E+1423,000 1.89E+14 10,000 PhMe-2.0 + H₂O → PhMe-2.1 + MeOH 1.42E+14 23,0001.42E+14 10,000 PhMe-2.1 + H₂O → PhMe-2.2 + MeOH 7.08E+13 23,0007.08E+13 10,000 PhMe-1.2 + PhMe-2.2 → PhMe-3.2 + H₂O 5.67E+13 23,0005.67E+13 10,000 PhMe-1.2 + PhMe-3.2 → PhMe-4.2 + H₂O 1.13E+13 23,0001.13E+13 10,000 2 PhMe-2.2 → PhMe-4.2 + H₂O 2.27E+12 23,000 2.27E+1210,000wherein Ph represents a phenyl group, Me represents a methyl group andPhMe-X. Y indicates a silane having a DP of X and where Y indicates thenumber of hydroxyl groups formed by the corresponding hydrolysis. Thus,for example, PhMe-1.0 is monomeric phenylmethyldimethoxysilane, PhMe-1.2is (Ph)(Me)Si(OH)2, PhMe-2.0 is the dimer(Ph)(Me)(MeO)SiOSi(OMe)(Me)(Ph), and so on.

-   (2) (α) for phenylmethyldimethoxysilane and its oligomers (PM)    and (a) for water (H2O):

α_(H2O)=0.30

α_(PM)=0.75

-   (3) Amount of initial fluid as a percentage of the interstitial    volume is 108%-   (4) Layer zero restriction ratio is 3.5%, and-   (5) Extent of the halo:

Peak of halo is 2% void in insulation;

Standard deviation of the halo void distribution is 71 mils;

Peak is located at a radius of 830 mils

In order to further clarify the curve-fitting of the parameters to theactual data, the following discussion is believed helpful. Again, withreference to FIG. 14, after the total concentration ofphenylmethyldimethoxysilaneand its oligomers peaks at about 10 days, therate of decay of the concentration of the phenylmethyldimethoxysilaneand its oligomers is most dependent on the reaction rates of conversionof monomer to the various oligomers. These reaction rates, in turn, aremost dependent on the reaction kinetics and the concentration of waterand catalyst available across the radius of the cable. If the modeledreactions proceed more rapidly than exhibited by the actual data, thenthe reaction rate constant, or the concentration of the water availablefor reaction, in the simulation is reduced.

The water concentration is dependent upon the amount of water present inthe insulation, including the halo which is always present in agedcable, and the amount of water in the conductor shield before treatment.Even more importantly, this concentration depends upon α_(water), asdefined in the description of Section 400, above, which largelydetermines the rate at which water ingresses from the outside into thecable throughout the simulation. If there were no deviation from idealsolution behavior, then water would be virtually excluded from cablesince it has a much lower equilibrium concentration than thealkoxysilane (i.e., if α_(water)=1, then there would be very littlepenetration by water; if α_(water)=0, then the presence of othercomponents would not affect water permeation). Two other independentdata points provide constraints on the water availability and thereaction rates. The first constraining data point is the indication thatan anhydrous, or largely water-free, environment persists for some timein the interstices of cables treated with the prior art materials (i.e.,phenylmethyldimethoxysilane in this case). See, for example, “Failuresin Silicone-treated German Cables Due to an unusual Aluminum-MethanolReaction”, Bertini, Presented to the Transnational Luncheon of the ICC,Oct. 29, 2002. If α_(water) is too low, or the reaction rate is tooslow, water will permeate into the strands and an anhydrous environmentwill never be achieved. The second constraint was supplied by thepreviously cited Kleyer and Chatterton paper, when they wrote:

-   -   “The presence of the water reactive functionality of        phenylmethyldimethoxysilane within the insulation was confirmed        by microscopic infrared spectroscopy (SiOMe band at 1190 cm⁻¹)        through 54 days.”

In other words, methoxy groups were still observable by micro-IR at 54days, but were no longer observed at 67 days. The reaction rate of thesimulation is constrained by the practical observation that allIR-measurable quantities of methoxy functionality must disappear in the13 days between 54 and 67 days.

These two constraints, along with FIG. 9 data, are used to establishα_(awater) and the chemical kinetics, which, in turn, largely determinethe slope of the curve in FIG. 14 between the peak (at about 10 days)and the point at 54 days. The reaction rates and the α_(water) wereestablished by a regression fit of the refined Kleyer data. The point atwhich the curve in FIG. 14 flattens somewhat is determined primarily bythe amount of the originally supplied fluid which exudes un-reacted orunder-reacted (i.e., no condensation to form oligomers). In thisillustration, exuded, un-reacted or under-reacted fluid encompassesmonomeric species and hydrolysis derivatives ofphenylmethyldimethoxysilane, specifically including those monomers withonly methoxy ligands, only hydroxyl ligands, and those with one eachmethoxy and hydroxyl, which exude from the insulation. Vincentdemonstrated (see Table 2 of U.S. Pat. No. 4,766,011) that, withoutcatalyst, there was no observable condensation of monomer in thepresence of water for the phenylmethyldimethoxysilane monomer employedby Kleyer and Chatterton. Hence, the reaction rate without catalyst isinconsequentially small.

The 194-day plateau and slow decay region, from day 54 to day 248, isdetermined by the rate of exudation of the condensing oligomer. Duringthis period, there is a steady flux of several oligomeric species out ofthe insulation, and for a while, a corresponding approximately equalflux into the insulation of the fluid remaining in the conductorinterstices and the conductor shield. Once the latter supply is nearlydepleted, the flux into the insulation begins to decrease and the totalconcentration therein begins to decrease along with it. Those skilled inthe art will recognize that, as the total concentration begins todecrease, the exudation out of the insulation also slows. This finalperiod is well described as an exponential decay to zero.

Fitting of the last 248 day point depends almost entirely on thepermeation rate of the dynamic mix of oligomers. As describedpreviously, Chatterton and Bertini provide permeation equations formonomer, dimer and tetramer. The dimer and tetramer were terminated withmethyl groups to determine experimental diffusion rates. This does notexactly correspond to the real-world case where these oligomers aregenerally terminated with hydroxyl groups or potentially cyclized. Evenwith these differences, reasonable interpolations and extrapolations toother members of the homologous series of oligomers (e.g. linear trimerand pentamer) can be readily made by those skilled in the art. Thedistribution of homologous oligomers can thus be determined by thetransition time from the plateau period to the exponential decay periodof FIG. 14. For example, if a simulation predicted that theconcentration decreased such that the resulting curve fell to the leftof, and below, the measured value (e.g. Sim 32 in FIG. 14), then thedynamic average degree of polymerization (DP) would have to beincreased. On the other hand, if the simulated line fell above, and tothe right of, the measured value (e.g. Sim 35), the dynamic DP wouldhave to be decreased. These dynamic DP values would in turn be increasedor decreased by increasing or decreasing the respective reaction ratesof condensation to higher oligomers. The aforementioned Kleyer andChatterton paper provides guidance on the subject when they report:

-   -   “The data confirmed that oligomerization occurs within the        strands, providing a polymeric distribution through a degree of        polymerization (DP) of eight or more.”        Those familiar with methoxysilane hydroysis will appreciate that        a statistical distribution of DPs is formed, driven by chemical        reaction considerations. Yet another constraining consideration        is the average concentration in the insulation during the period        from 54 to 248 days. As the DP increases, the equilibrium        concentration due to lowered solubility decreases and hence a        simulation falling below the 54 day and 67 day data points        implies that the average DP is too great while a simulation        curving above those two points would imply an average DP that is        too low.

All other variables not adjusted as empirical constants in the previousparagraphs which are required to complete the simulation were measuredby experimental means and/or were obtained from published results.

1. A computer simulation method for simulating an electrical cablehaving a stranded conductor surrounded by a conductor shield encased inan insulation jacket and having an interstitial void volume in theregion of the conductor injected with a fluid composition comprising atleast one dielectric enhancement fluid component so as to at leastpartially fill the interstitial void volume at an initial time t=0, thesimulation method comprising: for a selected length of the simulatedcable, defining a plurality of radially arranged finite volumesextending the selected length of the simulated cable; for each of aplurality of different selected incremental time periods occurring aftert=0: estimating the radial temperature of each finite volume;calculating the diffusion properties of the dielectric enhancement fluidcomponent within each finite volume using the estimated radialtemperature; calculating the mass flux from one finite volume to anotherfinite volume for the dielectric enhancement fluid component within thefinite volumes; and combining the calculated change in mass of thedielectric enhancement fluid component within each finite volume withthe calculated mass flux between each adjacent finite volume for thedielectric enhancement fluid component within the finite volumes todetermine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; and outputting the value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume.
 2. The computer simulation method of claim 1, furtherincluding using the outputted value of the new concentration for thedielectric enhancement fluid component within each finite volume todetermine a calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for at least one time aftert=0, and using the calculated concentration profile to select a suitablefluid composition for injection into the electrical cable beingsimulated.
 3. The computer simulation method of claim 2, furtherincluding providing an empirical model of the dielectric performance ofthe simulated cable as a function of concentration of the dielectricenhancement fluid component, and using the empirical model and thecalculated concentration profile for the dielectric enhancement fluidcomponent within the conductor shield and the insulation jacket of thesimulated cable to determine an estimate of dielectric performancechanges for at least one time after t=0.
 4. The computer simulationmethod of claim 1 wherein the finite volumes are a plurality of coaxialcylinders extending the selected length of the simulated cable.
 5. Thecomputer simulation method of claim 1, further including: using theoutputted value of the new concentration for the dielectric enhancementfluid component within each finite volume to determine a firstcalculated concentration profile for the dielectric enhancement fluidcomponent within the conductor shield and the insulation jacket of thesimulated cable for a selected time after t=0; for each of a pluralityof different selected incremental time periods occurring after t=0 usinga selected constant radial temperature for each finite volume:calculating the diffusion properties of the dielectric enhancement fluidcomponent within each finite volume; calculating the mass flux from onefinite volume to another finite volume for the dielectric enhancementfluid component within the finite volumes; and combining the calculatedchange in mass of the dielectric enhancement fluid component within eachfinite volume with the calculated mass flux between each adjacent finitevolume for the dielectric enhancement fluid component within the finitevolumes to determine a new concentration for the dielectric enhancementfluid component within each finite volume; outputting the value of thenew concentration for the dielectric enhancement fluid component withineach finite volume using the selected constant radial temperature; usingthe outputted value of the new concentration for the dielectricenhancement fluid component within each finite volume using the selectedconstant radial temperature to determine a second calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable for the selected time after t=0; determining if the secondcalculated concentration profile approximates the first calculatedconcentration profile; and using the selected constant radialtemperature as a flux-weighted temperature if the second calculatedconcentration profile approximates the first calculated concentrationprofile.
 6. The computer simulation method of claim 5, wherein if thesecond calculated concentration profile does not approximate the firstcalculated concentration profile, selecting a different constant radialtemperature for each finite volume to use for each of the plurality ofdifferent selected incremental time periods occurring after t=0, untilthe second calculated concentration profile approximates the firstcalculated concentration profile.
 7. The computer simulation method ofclaim 6 wherein the flux-weighted temperature is used to select asuitable fluid composition for injection into the electrical cable beingsimulated.
 8. The computer simulation method of claim 1, furtherincluding: using the outputted value of the new concentration for thedielectric enhancement fluid component within each finite volume todetermine a first calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for a selected time after t=0;determining a constant radial temperature for each finite volume thatresults in a second calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for the selected time after t=0that approximates the first calculated concentration profile, by:selecting a constant radial temperature for each finite volume to use indetermining the second calculated concentration profile; using theselected constant radial temperature, for each of a plurality ofdifferent selected incremental time periods occurring after t=0:calculating the diffusion properties of the dielectric enhancement fluidcomponent within each finite volume; calculating the mass flux from onefinite volume to another finite volume for the dielectric enhancementfluid component within the finite volumes; combining the calculatedchange in mass of the dielectric enhancement fluid component within eachfinite volume with the calculated mass flux between each adjacent finitevolume for the dielectric enhancement fluid component within the finitevolumes to determine a new concentration for the dielectric enhancementfluid component within each finite volume; outputting the value of thenew concentration for the dielectric enhancement fluid component withineach finite volume using the selected constant radial temperature; usingthe outputted value of the new concentration for the dielectricenhancement fluid component within each finite volume using the selectedconstant radial temperature to determine the second calculatedconcentration profile; determining if the second calculatedconcentration profile approximates the first calculated concentrationprofile; if the selected constant radial temperature does not result inthe second calculated concentration profile being determined toapproximate the first calculated concentration profile, selecting a newconstant radial temperature to use in determining the second calculatedconcentration profile; and if the selected constant radial temperaturedoes result in the second calculated concentration profile beingdetermined to approximate the first calculated concentration profile,using the selected constant radial temperature as a flux-weightedtemperature.
 9. A computer simulation method for simulating anelectrical cable having a stranded conductor surrounded by a conductorshield encased in an insulation jacket and having an interstitial voidvolume in the region of the conductor injected with a fluid compositioncomprising at least one dielectric enhancement fluid component so as toat least partially fill the interstitial void volume at an initial time,the simulation method comprising: for a selected length of the simulatedcable, defining a plurality of radially arranged finite volumesextending the selected length of the simulated cable; estimating theradial temperature of each finite volume; for a selected time periodafter the initial time, performing at least once each of: calculatingthe diffusion properties of the dielectric enhancement fluid componentwithin each finite volume using the estimated radial temperature;calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid component within the finitevolumes; and combining the calculated change in mass of the dielectricenhancement fluid component within each finite volume with thecalculated mass flux between each adjacent finite volume for thedielectric enhancement fluid component within the finite volumes todetermine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; and outputting the value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume.
 10. The computer simulation method of claim 9, furtherincluding: using the outputted value of the new concentration for thedielectric enhancement fluid component within each finite volume todetermine a first calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for the selected time periodafter the initial time; determining a constant radial temperature foreach finite volume that results in a second calculated concentrationprofile for the dielectric enhancement fluid component within theconductor shield and the insulation jacket of the simulated cable forthe selected time period after the initial time that approximates thefirst calculated concentration profile, by: selecting a constant radialtemperature for each finite volume to use in determining the secondcalculated concentration profile; using the selected constant radialtemperature, for a selected time period after the initial time,performing at least once each of: calculating the diffusion propertiesof the dielectric enhancement fluid component within each finite volume;calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid component within the finitevolumes; combining the calculated change in mass of the dielectricenhancement fluid component within each finite volume with thecalculated mass flux between each adjacent finite volume for thedielectric enhancement fluid component within the finite volumes todetermine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; outputting the value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume using the selected constant radial temperature; using theoutputted value of the new concentration for the dielectric enhancementfluid component within each finite volume using the selected constantradial temperature to determine the second calculated concentrationprofile; determining if the second calculated concentration profileapproximates the first calculated concentration profile; if the selectedconstant radial temperature does not result in the second calculatedconcentration profile being determined to approximate the firstcalculated concentration profile, selecting a new constant radialtemperature to use in determining the second calculated concentrationprofile; and if the selected constant radial temperature does result inthe second calculated concentration profile being determined toapproximate the first calculated concentration profile, using theselected constant radial temperature as a flux-weighted temperature. 11.The computer simulation method of claim 10 wherein the flux-weightedtemperature is used to select a suitable fluid composition for injectioninto the electrical cable being simulated.
 12. A computer simulationmethod for simulating an electrical cable having a stranded conductorsurrounded by a conductor shield encased in an insulation jacket andhaving an interstitial void volume in the region of the conductorinjected with a fluid composition comprising at least one dielectricenhancement fluid component so as to at least partially fill theinterstitial void volume at an initial time, the simulation methodcomprising: for a selected length of the simulated cable, defining aplurality of radially arranged finite volumes extending the selectedlength of the simulated cable; estimating the radial temperature of eachfinite volume; for a selected time period after the initial time,performing at least once each of: calculating the diffusion propertiesof the dielectric enhancement fluid component within each finite volumeusing the estimated radial temperature; calculating the mass flux fromone finite volume to another finite volume for the dielectricenhancement fluid component within the finite volumes; and combining thecalculated change in mass of the dielectric enhancement fluid componentwithin each finite volume with the calculated mass flux between eachadjacent finite volume for the dielectric enhancement fluid componentwithin the finite volumes to determine a new concentration for thedielectric enhancement fluid component within each finite volume; usingthe new concentration for the dielectric enhancement fluid componentwithin each finite volume to determine a calculated concentrationprofile for the dielectric enhancement fluid component within theconductor shield and the insulation jacket of the simulated cable forthe selected time period after the initial time; and using thecalculated concentration profile to select a suitable fluid compositionfor injection into the electrical cable being simulated.
 13. Thecomputer simulation method of claim 12, further including providing anempirical model of the dielectric performance of the simulated cable asa function of concentration of the dielectric enhancement fluidcomponent, and using the empirical model and the calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable to determine an estimate of dielectric performance changes fortimes after the initial time.
 14. A computer simulation method forsimulating an electrical cable having a stranded conductor surrounded bya conductor shield encased in an insulation jacket and having aninterstitial void volume in the region of the conductor injected with afluid composition comprising a plurality of dielectric enhancement fluidcomponents so as to at least partially fill the interstitial void volumeat an initial time t=0, the simulation method comprising: for a selectedlength of the simulated cable, defining a plurality of radially arrangedfinite volumes extending the selected length of the simulated cable;estimating the radial temperature of each finite volume; for each of aplurality of different selected incremental time periods occurring aftert=0: calculating the diffusion properties of the dielectric enhancementfluid components within each finite volume using the estimated radialtemperature; calculating the mass flux from one finite volume to anotherfinite volume for the dielectric enhancement fluid components within thefinite volumes; and combining the calculated change in mass of thedielectric enhancement fluid components within each finite volume withthe calculated mass flux between each adjacent finite volume for thedielectric enhancement fluid components within the finite volumes todetermine new concentrations for the dielectric enhancement fluidcomponents within each finite volume; and outputting the values of thenew concentrations for the dielectric enhancement fluid componentswithin each finite volume.
 15. The computer simulation method of claim14, further including: using the outputted values of the newconcentrations for the dielectric enhancement fluid components withineach finite volume to determine a first combined calculatedconcentration profile for the dielectric enhancement fluid componentswithin the conductor shield and the insulation jacket of the simulatedcable for a selected time after t=0; determining a constant radialtemperature for each finite volume that results in a second combinedcalculated concentration profile for the dielectric enhancement fluidcomponents within the conductor shield and the insulation jacket of thesimulated cable for the selected time after t=0 that approximates thefirst calculated concentration profile, by: selecting a constant radialtemperature for each finite volume to use in determining the secondcombined calculated concentration profile; using the selected constantradial temperature, for each of a plurality of different selectedincremental time periods occurring after t=0: calculating the diffusionproperties of the dielectric enhancement fluid component within eachfinite volume; calculating the mass flux from one finite volume toanother finite volume for the dielectric enhancement fluid componentwithin the finite volumes; combining the calculated change in mass ofthe dielectric enhancement fluid component within each finite volumewith the calculated mass flux between each adjacent finite volume forthe dielectric enhancement fluid components within the finite volumes todetermine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; outputting the values of the newconcentrations for the dielectric enhancement fluid components withineach finite volume using the selected constant radial temperature; usingthe outputted values of the new concentrations for the dielectricenhancement fluid components within each finite volume using theselected constant radial temperature to determine the second combinedcalculated concentration profile; determining if the second combinedcalculated concentration profile approximates the first combinedcalculated concentration profile; if the selected constant radialtemperature does not result in the second combined calculatedconcentration profile being determined to approximate the first combinedcalculated concentration profile, selecting a new constant radialtemperature to use in determining the second combined calculatedconcentration profile; and if the selected constant radial temperaturedoes result in the second combined calculated concentration profilebeing determined to approximate the first combined calculatedconcentration profile, using the selected constant radial temperature asa flux-weighted temperature.
 16. A computer simulation method forsimulating an electrical cable having a stranded conductor surrounded bya conductor shield encased in an insulation jacket and having aninterstitial void volume in the region of the conductor injected with afluid composition comprising a plurality of dielectric enhancement fluidcomponents so as to at least partially fill the interstitial void volumeat an initial time t=0, the simulation method comprising: for a selectedlength of the simulated cable, defining a plurality of radially arrangedfinite volumes extending the selected length of the simulated cable;estimating the radial temperature of each finite volume; for each of aplurality of different selected incremental time periods occurring aftert=0: calculating the diffusion properties of the dielectric enhancementfluid components within each finite volume using the estimated radialtemperature; calculating the mass flux from one finite volume to anotherfinite volume for the dielectric enhancement fluid components within thefinite volumes; and combining the calculated change in mass of thedielectric enhancement fluid components within each finite volume withthe calculated mass flux between each adjacent finite volume for thedielectric enhancement fluid components within the finite volumes todetermine new concentrations for the dielectric enhancement fluidcomponents within each finite volume; and using the new concentrationsfor the dielectric enhancement fluid components within each finitevolume to determine a calculated concentration profile for each of thedielectric enhancement fluid components within the conductor shield andthe insulation jacket of the simulated cable for at least one time aftert=0; and using the calculated concentration profile for each of thedielectric enhancement fluid components to select a suitable fluidcomposition for injection into the electrical cable being simulated. 17.The computer simulation method of claim 16, further including providingan empirical model of the dielectric performance of the simulated cableas a function of concentrations of the dielectric enhancement fluidcomponents, and using the empirical model and the calculatedconcentration profiles for the dielectric enhancement fluid componentswithin the conductor shield and the insulation jacket of the simulatedcable to determine an estimate of dielectric performance changes fortimes after the initial time.
 18. A computer simulation method forsimulating an electrical cable having a stranded conductor surrounded bya conductor shield encased in an insulation jacket and having aninterstitial void volume in the region of the conductor injected with afluid composition comprising a plurality of dielectric enhancement fluidcomponents so as to at least partially fill the interstitial void volumeat an initial time, the simulation method comprising: for a selectedlength of the simulated cable, defining a plurality of radially arrangedfinite volumes extending the selected length of the simulated cable;estimating the radial temperature of each finite volume; for a selectedtime period after the initial time, performing at least once for each ofthe dielectric enhancement fluid components, each of: calculating thediffusion properties of the dielectric enhancement fluid componentswithin each finite volume using the estimated radial temperature;calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid components within the finitevolumes; and combining the calculated change in mass of the dielectricenhancement fluid components within each finite volume with thecalculated mass flux between each adjacent finite volume for thedielectric enhancement fluid components within the finite volumes todetermine new concentrations for the dielectric enhancement fluidcomponents within each finite volume; and outputting the values of thenew concentrations for the dielectric enhancement fluid componentswithin each finite volume.
 19. The computer simulation method of claim18, further including using the outputted values of the newconcentrations for the dielectric enhancement fluid components withineach finite volume to determine for each of the dielectric enhancementfluid components a calculated concentration profile within the conductorshield and the insulation jacket of the simulated cable for the selectedtime period after the initial time, and using the calculatedconcentration profiles to select a suitable fluid composition forinjection into the electrical cable being simulated.
 20. The computersimulation method of claim 19, further including providing an empiricalmodel of the dielectric performance of the simulated cable as a functionof concentrations of the dielectric enhancement fluid components, andusing the empirical model and the calculated concentration profiles forthe dielectric enhancement fluid components within the conductor shieldand the insulation jacket of the simulated cable to determine anestimate of dielectric performance changes for times after the initialtime.
 21. The computer simulation method of claim 18, further including:using the outputted values of the new concentrations for the dielectricenhancement fluid components within each finite volume to determine afirst combined calculated concentration profile for the dielectricenhancement fluid components within the conductor shield and theinsulation jacket of the simulated cable for the selected time periodafter the initial time; determining a constant radial temperature foreach finite volume that results in a second combined calculatedconcentration profile for the dielectric enhancement fluid componentswithin the conductor shield and the insulation jacket of the simulatedcable for the selected time period after the initial time thatapproximates the first combined calculated concentration profile, by:selecting a constant radial temperature for each finite volume to use indetermining the second combined calculated concentration profile; usingthe selected constant radial temperature, for the selected time periodafter the initial time: calculating the diffusion properties of thedielectric enhancement fluid component within each finite volume;calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid component within the finitevolumes; combining the calculated change in mass of the dielectricenhancement fluid component within each finite volume with thecalculated mass flux between each adjacent finite volume for thedielectric enhancement fluid components within the finite volumes todetermine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; outputting the values of the newconcentrations for the dielectric enhancement fluid components withineach finite volume using the selected constant radial temperature; usingthe outputted values of the new concentrations for the dielectricenhancement fluid components within each finite volume using theselected constant radial temperature to determine the second combinedcalculated concentration profile; determining if the second combinedcalculated concentration profile approximates the first combinedcalculated concentration profile; if the selected constant radialtemperature does not result in the second combined calculatedconcentration profile being determined to approximate the first combinedcalculated concentration profile, selecting a new constant radialtemperature to use in determining the second combined calculatedconcentration profile; and if the selected constant radial temperaturedoes result in the second combined calculated concentration profilebeing determined to approximate the first combined calculatedconcentration profile, using the selected constant radial temperature asa flux-weighted temperature.
 22. A computer simulation system forsimulating an electrical cable having a stranded conductor surrounded bya conductor shield encased in an insulation jacket and having aninterstitial void volume in the region of the conductor injected with afluid composition comprising at least one dielectric enhancement fluidcomponent so as to at least partially fill the interstitial void volumeat an initial time, the system comprising: means for defining aplurality of radially arranged finite volumes extending the selectedlength of the simulated cable for a selected length of the simulatedcable; means for estimating the radial temperature of each finitevolume; means for calculating the change in mass of the dielectricenhancement fluid component within each finite volume due to chemicalreactions for a selected time period after the initial time using theestimated radial temperature of each finite volume; means forcalculating the diffusion properties of the dielectric enhancement fluidcomponent within each finite volume for the selected time period afterthe initial time using the estimated radial temperature of each finitevolume; means for calculating the mass flux from one finite volume toanother finite volume for the dielectric enhancement fluid componentwithin the finite volumes for the selected time period after the initialtime using the estimated radial temperature of each finite volume; meansfor combining the calculated change in mass of the dielectricenhancement fluid component within each finite volume due to chemicalreactions with the calculated mass flux between each adjacent finitevolume for the dielectric enhancement fluid component within the finitevolumes for the selected time period after the initial time to determinea new concentration for the dielectric enhancement fluid componentwithin each finite volume; and means for outputting the value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume.
 23. The computer simulation system of claim 22, furtherincluding means for using the outputted value of the new concentrationfor the dielectric enhancement fluid component within each finite volumeto determine a calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for the selected time periodafter the initial time to select a suitable fluid composition forinjection into the electrical cable being simulated.
 24. The computersimulation system of claim 23, further including means for storing anempirical model of the dielectric performance of the simulated cable asa function of concentration of the dielectric enhancement fluidcomponent, and means for using the empirical model and the calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable to determine an estimate of dielectric performance changes fortimes after the initial time.
 25. The computer simulation system ofclaim 22, further including: means for using the outputted value of thenew concentration for the dielectric enhancement fluid component withineach finite volume to determine a first calculated concentration profilefor the dielectric enhancement fluid component within the conductorshield and the insulation jacket of the simulated cable for the selectedtime period after the initial time; means for storing a constant radialtemperature for each finite volume that results in a second calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable for the selected time period after the initial time thatapproximates the first calculated concentration profile; means forcalculating the change in mass of the dielectric enhancement fluidcomponent within each finite volume due to chemical reactions for theselected time period after the initial time using the selected constantradial temperature; means for calculating the diffusion properties ofthe dielectric enhancement fluid component within each finite volume forthe selected time period after the initial time using the selectedconstant radial temperature; means for calculating the mass flux fromone finite volume to another finite volume for the dielectricenhancement fluid component within the finite volumes for the selectedtime period after the initial time using the selected constant radialtemperature; means for combining the calculated change in mass of thedielectric enhancement fluid component within each finite volume due tochemical reactions with the calculated mass flux between each adjacentfinite volume for the dielectric enhancement fluid component within thefinite volumes for the selected time period after the initial time todetermine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; means for outputting the value ofthe new concentration for the dielectric enhancement fluid componentwithin each finite volume using the selected constant radialtemperature; means for using the outputted value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume using the selected constant radial temperature todetermine the second calculated concentration profile; and means fordetermining if the second calculated concentration profile approximatesthe first calculated concentration profile, and if the selected constantradial temperature does not result in the second calculatedconcentration profile being determined to approximate the firstcalculated concentration profile, selecting a new constant radialtemperature to use in determining the second calculated concentrationprofile, and if the selected constant radial temperature does result inthe second calculated concentration profile being determined toapproximate the first calculated concentration profile, using theselected constant radial temperature as a flux-weighted temperature. 26.A computer simulation system for simulating an electrical cable having astranded conductor surrounded by a conductor shield encased in aninsulation jacket and having an interstitial void volume in the regionof the conductor injected with a fluid composition comprising at leastone dielectric enhancement fluid component so as to at least partiallyfill the interstitial void volume at an initial time, the systemcomprising: means for defining a plurality of radially arranged finitevolumes extending the selected length of the simulated cable for aselected length of the simulated cable; means for estimating the radialtemperature of each finite volume; means for calculating the diffusionproperties of the dielectric enhancement fluid component within eachfinite volume for a selected time period after the initial time usingthe estimated radial temperature; means for calculating the mass fluxfrom one finite volume to another finite volume for the dielectricenhancement fluid component within the finite volumes for the selectedtime period after the initial time; means for combining the calculatedchange in mass of the dielectric enhancement fluid component within eachfinite volume with the calculated mass flux between each adjacent finitevolume for the dielectric enhancement fluid component within the finitevolumes for the selected time period after the initial time to determinea new concentration for the dielectric enhancement fluid componentwithin each finite volume; and means for outputting the value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume.
 27. The computer simulation system of claim 26, furtherincluding means for using the outputted value of the new concentrationfor the dielectric enhancement fluid component within each finite volumeto determine a calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for the selected time periodafter the initial time to select a suitable fluid composition forinjection into the electrical cable being simulated.
 28. The computersimulation system of claim 27, further including means for storing anempirical model of the dielectric performance of the simulated cable asa function of concentration of the dielectric enhancement fluidcomponent, and means for using the empirical model and the calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable to determine an estimate of dielectric performance changes fortimes after the initial time.
 29. The computer simulation system ofclaim 26, further including: means for using the outputted value of thenew concentration for the dielectric enhancement fluid component withineach finite volume to determine a first calculated concentration profilefor the dielectric enhancement fluid component within the conductorshield and the insulation jacket of the simulated cable for the selectedtime period after the initial time; means for storing a constant radialtemperature for each finite volume that results in a second calculatedconcentration profile for the dielectric enhancement fluid componentwithin the conductor shield and the insulation jacket of the simulatedcable for the selected time period after the initial time thatapproximates the first calculated concentration profile; means forcalculating the diffusion properties of the dielectric enhancement fluidcomponent within each finite volume for the selected time period afterthe initial time using the selected constant radial temperature; meansfor calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid component within the finitevolumes for the selected time period after the initial time using theselected constant radial temperature; means for combining the calculatedchange in mass of the dielectric enhancement fluid component within eachfinite volume with the calculated mass flux between each adjacent finitevolume for the dielectric enhancement fluid component within the finitevolumes for the selected time period after the initial time to determinea new concentration for the dielectric enhancement fluid componentwithin each finite volume; means for outputting the value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume using the selected constant radial temperature; means forusing the outputted value of the new concentration for the dielectricenhancement fluid component within each finite volume using the selectedconstant radial temperature to determine the second calculatedconcentration profile; and means for determining if the secondcalculated concentration profile approximates the first calculatedconcentration profile, and if the selected constant radial temperaturedoes not result in the second calculated concentration profile beingdetermined to approximate the first calculated concentration profile,selecting a new constant radial temperature to use in determining thesecond calculated concentration profile, and if the selected constantradial temperature does result in the second calculated concentrationprofile being determined to approximate the first calculatedconcentration profile, using the selected constant radial temperature asa flux-weighted temperature.
 30. A computer-readable medium whoseinstructions cause a computer system to simulate an electrical cablehaving a stranded conductor surrounded by a conductor shield encased inan insulation jacket and having an interstitial void volume in theregion of the conductor injected with a fluid composition comprising atleast one dielectric enhancement fluid component so as to at leastpartially fill the interstitial void volume at an initial time, by:defining a plurality of radially arranged finite volumes extending theselected length of the simulated cable for a selected length of thesimulated cable; estimating the radial temperature of each finitevolume; for a selected time period after the initial time, performing atleast once each of: calculating the change in mass of the dielectricenhancement fluid component within each finite volume due to chemicalreactions using the estimated radial temperature; calculating thediffusion properties of the dielectric enhancement fluid componentwithin each finite volume using the estimated radial temperature;calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid component within the finitevolumes; and combining the calculated change in mass of the dielectricenhancement fluid component within each finite volume due to chemicalreactions with the calculated mass flux between each adjacent finitevolume for the dielectric enhancement fluid component within the finitevolumes to determine a new concentration for the dielectric enhancementfluid component within each finite volume; and outputting the value ofthe new concentration for the dielectric enhancement fluid componentwithin each finite volume.
 31. The computer-readable medium of claim 30whose instructions cause the computer system to simulate the electricalcable by using the outputted value of the new concentration for thedielectric enhancement fluid component within each finite volume todetermine a calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for the selected time periodafter the initial time to select a suitable fluid composition forinjection into the electrical cable being simulated.
 32. Thecomputer-readable medium of claim 31 for use with the computer systemhaving a stored empirical model of the dielectric performance of thesimulated cable as a function of concentration of the dielectricenhancement fluid component, whose instructions cause the computersystem to simulate the electrical cable by using the empirical model andthe calculated concentration profile for the dielectric enhancementfluid component within the conductor shield and the insulation jacket ofthe simulated cable to determine an estimate of dielectric performancechanges for times after the initial time.
 33. The computer-readablemedium of claim 30 whose instructions cause the computer system tosimulate the electrical cable by: using the outputted value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume to determine a first calculated concentration profile forthe dielectric enhancement fluid component within the conductor shieldand the insulation jacket of the simulated cable for the selected timeperiod after the initial time; determining a constant radial temperaturefor each finite volume that results in a second calculated concentrationprofile for the dielectric enhancement fluid component within theconductor shield and the insulation jacket of the simulated cable forthe selected time period after the initial time that approximates thefirst calculated concentration profile, by: selecting a constant radialtemperature for each finite volume to use in determining the secondcalculated concentration profile; using the selected constant radialtemperature, for a selected time period after the initial time,performing at least once each of: calculating the change in mass of thedielectric enhancement fluid component within each finite volume due tochemical reactions; calculating the diffusion properties of thedielectric enhancement fluid component within each finite volume;calculating the mass flux from one finite volume to another finitevolume for the dielectric enhancement fluid component within the finitevolumes; combining the calculated change in mass of the dielectricenhancement fluid component within each finite volume due to chemicalreactions with the calculated mass flux between each adjacent finitevolume for the dielectric enhancement fluid component within the finitevolumes to determine a new concentration for the dielectric enhancementfluid component within each finite volume; outputting the value of thenew concentration for the dielectric enhancement fluid component withineach finite volume using the selected constant radial temperature; usingthe outputted value of the new concentration for the dielectricenhancement fluid component within each finite volume using the selectedconstant radial temperature to determine the second calculatedconcentration profile; determining if the second calculatedconcentration profile approximates the first calculated concentrationprofile; if the selected constant radial temperature does not result inthe second calculated concentration profile being determined toapproximate the first calculated concentration profile, selecting a newconstant radial temperature to use in determining the second calculatedconcentration profile; and if the selected constant radial temperaturedoes result in the second calculated concentration profile beingdetermined to approximate the first calculated concentration profile,using the selected constant radial temperature as a flux-weightedtemperature.
 34. A computer-readable medium whose instructions cause acomputer system to simulate an electrical cable having a strandedconductor surrounded by a conductor shield encased in an insulationjacket and having an interstitial void volume in the region of theconductor injected with a fluid composition comprising at least onedielectric enhancement fluid component so as to at least partially fillthe interstitial void volume at an initial time, by: defining aplurality of radially arranged finite volumes extending the selectedlength of the simulated cable for a selected length of the simulatedcable; estimating the radial temperature of each finite volume; for aselected time period after the initial time, performing at least onceeach of: calculating the diffusion properties of the dielectricenhancement fluid component within each finite volume using theestimated radial temperature; calculating the mass flux from one finitevolume to another finite volume for the dielectric enhancement fluidcomponent within the finite volumes; and combining the calculated changein mass of the dielectric enhancement fluid component within each finitevolume with the calculated mass flux between each adjacent finite volumefor the dielectric enhancement fluid component within the finite volumesto determine a new concentration for the dielectric enhancement fluidcomponent within each finite volume; and outputting the value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume.
 35. The computer-readable medium of claim 34 whoseinstructions cause the computer system to simulate the electrical cableby using the outputted value of the new concentration for the dielectricenhancement fluid component within each finite volume to determine acalculated concentration profile for the dielectric enhancement fluidcomponent within the conductor shield and the insulation jacket of thesimulated cable for the selected time period after the initial time toselect a suitable fluid composition for injection into the electricalcable being simulated.
 36. The computer-readable medium of claim 35 foruse with the computer system having a stored empirical model of thedielectric performance of the simulated cable as a function ofconcentration of the dielectric enhancement fluid component, whoseinstructions cause the computer system to simulate the electrical cableby using the empirical model and the calculated concentration profilefor the dielectric enhancement fluid component within the conductorshield and the insulation jacket of the simulated cable to determine anestimate of dielectric performance changes for times after the initialtime.
 37. The computer-readable medium of claim 34 whose instructionscause the computer system to simulate the electrical cable by: using theoutputted value of the new concentration for the dielectric enhancementfluid component within each finite volume to determine a firstcalculated concentration profile for the dielectric enhancement fluidcomponent within the conductor shield and the insulation jacket of thesimulated cable for the selected time period after the initial time;determining a constant radial temperature for each finite volume thatresults in a second calculated concentration profile for the dielectricenhancement fluid component within the conductor shield and theinsulation jacket of the simulated cable for the selected time periodafter the initial time that approximates the first calculatedconcentration profile, by: selecting a constant radial temperature foreach finite volume to use in determining the second calculatedconcentration profile; using the selected constant radial temperature,for a selected time period after the initial time, performing at leastonce each of: calculating the diffusion properties of the dielectricenhancement fluid component within each finite volume; calculating themass flux from one finite volume to another finite volume for thedielectric enhancement fluid component within the finite volumes;combining the calculated change in mass of the dielectric enhancementfluid component within each finite volume with the calculated mass fluxbetween each adjacent finite volume for the dielectric enhancement fluidcomponent within the finite volumes to determine a new concentration forthe dielectric enhancement fluid component within each finite volume;outputting the value of the new concentration for the dielectricenhancement fluid component within each finite volume using the selectedconstant radial temperature; using the outputted value of the newconcentration for the dielectric enhancement fluid component within eachfinite volume using the selected constant radial temperature todetermine the second calculated concentration profile; determining ifthe second calculated concentration profile approximates the firstcalculated concentration profile; if the selected constant radialtemperature does not result in the second calculated concentrationprofile being determined to approximate the first calculatedconcentration profile, selecting a new constant radial temperature touse in determining the second calculated concentration profile; and ifthe selected constant radial temperature does result in the secondcalculated concentration profile being determined to approximate thefirst calculated concentration profile, using the selected constantradial temperature as a flux-weighted temperature.